#N Stamp collection #C A collection of 650 oscillators of 83 different periods from 1 #C to 40894. #C #C The oscillators included here were found/built by many people over #C many years. I finished putting the collection together in August 1995, #C and have worked on this header file off and on since then. It's still #C incomplete and probably inaccurate, but I've decided to make it public #C anyway; if you find any errors or can fill in any of the blanks, please #C let me know. #C #C Since this collection was built, many new oscillators have been found. #C Most notably, in 1996 David Buckingham showed how to create tracks #C built from still-lifes through which Herschels can move. (See #C http://www.radicaleye.com/lifepage/patterns/bhept/bhept.html #C for Buckingham's description of this, and #C http://www.radicaleye.com/lifepage/patterns/p1/p1.html #C for Paul Callahan's discussion of using such conduits to build a stable #C glider reflector.) Using Herschel tracks, Buckingham obtained glider #C guns of all periods >= 62 and oscillators of all periods >= 61. Further #C work on Herschel tracks has been done by Buckingham, Paul Callahan, #C Dieter Leithner, and me; such tracks now give oscillators of all periods #C >=54, and guns of periods 54, 55, and 56. #C #C In addition, oscillators of several new smaller periods have been found, #C namely 17 (by me), 22 (by Noam Elkies, me, and Jason Summers), 27 (by #C Elkies), 33 (by Elkies and Jason Summers), 37 (by Nicolay Beluchenko), #C 39 (by Elkies), 49 (by Elkies), and 51 (by Beluchenko). (See #C http://www.radicaleye.com/DRH/nbt.html #C for many oscillators of small periods, including the only known p17s #C and the smallest known p22s.) There are 8 periods for which oscillators #C are still unknown as of early 2009: 19, 23, 31, 34, 38, 41, 43, and 53. #C (For period 34, we could use a noninteracting combination of p2 and p17 #C oscillators, but that's considered trivial.) #C #C Some new guns of smaller periods have also been found, namely 22 (by #C David Eppstein, based on Jason Summers's p22 oscillator), 24 and 48 (by #C Elkies) and 50 (by me, based on a p44 gun by Buckingham and a p50 #C oscillator by Elkies). These are shown (among others) at #C http://home.mieweb.com/jason/life/guns/ . #C Also see http://www.radicaleye.com/lifepage/patterns/p24gun/p24gun.html #C for discussion of the p24 gun, and #C http://www.radicaleye.com/DRH/gun44.50.html #C for the p50 gun and Buckingham's p44 gun. #C #C Building this collection would have been impossible without the help #C of many people. In addition to those who found the oscillators, I'd #C like to thank Alan Hensel, Bill Gosper, Robert Wainwright, #C Rich Schroeppel, and Jonathan Cooley for helpful suggestions, and #C Andrew Trevorrow for writing LifeLab, an excellent Macintosh program #C for building and running Life patterns. LifeLab's cross-platform #C successor, Golly, is available as freeware at http://golly.sf.net . #C #O Dean Hickerson, dean.hickerson@yahoo.com #C 2/2/2000; last updated 9/16/2000. URLs corrected #C and list of missing periods updated on 5/8/2009. #C #C ---------------------------------------------------------------------- #C #C Most lines of this header describe particular oscillators. Each entry #C begins with an identifying label, of the form "period.row.column"; #C row and column numbers start at zero. This is followed by the name of #C the oscillator (if any) in quotation marks, the discoverer and date of #C discovery (if known) in brackets, and perhaps a comment about the #C oscillator. For example: #C #C 2.0.0 "blinker" [JHC 3/70] Example of "+c*c" symmetry. This #C often occurs in a group of 4, known as a "traffic light", #C which arises, for example, from a T-tetromino. #C #C This indicates that the leftmost oscillator in the top row of the period 2 #C section is called a "blinker", and was found by John Conway in March 1970. #C The notation "+c*c" indicates the symmetry type of the oscillator, which #C is described later. #C #C Many oscillators were found by the following people or groups, so their #C names are abbreviated in this header: #C #C AF = Achim Flammenkamp #C AWH = Alan Hensel #C DIB = David Bell #C DJB = David Buckingham #C DRH = Dean Hickerson #C HH = Hartmut Holzwart #C JHC = John Conway #C MDN = Mark Niemiec #C NDE = Noam Elkies #C PC = Paul Callahan #C RCS = Rich Schroeppel #C RTW = Robert Wainwright #C RWG = Bill Gosper #C SN = Simon Norton #C JHC group = A group of people working with John Conway in the #C early 1970s, including Conway, S. R. Bourne, #C M. J. T. Guy, and Simon Norton. #C MIT group = A group of people at MIT during the early 1970s, #C including Robert April, Michael Beeler, Bill Gosper, #C Richard Howell, Rici Liknaitzky, Bill Mann, #C Rich Schroeppel, and Michael Speciner. #C #C Also, many of the common oscillators were found independently by many #C people; this is indicated by an asterisk in the name field. #C #C Here are definitions of some terminology and notation used below; for #C a more extensive glossary, see Stephen Silver's Life Lexicon, at #C http://www.argentum.freeserve.co.uk/lex_home.htm #C #C The 'rotor' constists of all cells in an oscillator which change state. #C The 'stator' constists of all cells which are alive in all generations. #C (These terms were introduced by Allan Wechsler in 1994.) #C #C An oscillator whose stator is large is often called a 'billiard table'; #C such oscillators are somewhat easier to find than others, so many are #C included in this collection. #C #C The 'period' of an oscillator (or spaceship) is the smallest positive #C integer P for which generation P of the object is congruent to and in #C the same orientation as generation 0. The 'mod' of an oscillator (or #C spaceship) is the smallest positive integer M for which generation M #C of the object is congruent to generation 0, but not necessarily in the #C same orientation. The quotient q=P/M is always either 1, 2, or 4. To #C specify both P and M, we often write "period P.M" or "period P/q". #C #C There are 43 types of symmetry that an oscillator can have, taking into #C account both the symmetry of a single generation and the change of #C orientation (if any) M generations later. There are 16 types of #C symmetry that a pattern can have in a single generation. Each of these #C is given a one or two character name, as follows: #C #C n no symmetry #C #C -c mirror symmetry across a horizontal axis through cell centers #C -e mirror symmetry across a horizontal axis through cell edges #C #C / mirror symmetry across one diagonal #C #C .c 180 degree rotational symmetry about a cell center #C .e 180 degree rotational symmetry about a cell edge #C .k 180 degree rotational symmetry about a cell corner #C #C +c mirror symmetry across horizontal and vertical axes meeting #C at a cell center #C +e mirror symmetry across horizontal and vertical axes meeting #C at a cell edge #C +k mirror symmetry across horizontal and vertical axes meeting #C at a cell corner #C #C xc mirror symmetry across 2 diagonals meeting at a cell center #C xk mirror symmetry across 2 diagonals meeting at a cell corner #C #C rc 90 degree rotational symmetry about a cell center #C rk 90 degree rotational symmetry about a cell corner #C #C *c 8-fold symmetry about a cell center #C *k 8-fold symmetry about a cell corner #C #C For a period P/1 object, specifying the symmetry of generation 0 tells #C us all there is to know about the oscillator's symmetry. For a period #C P/2 or P/4 object, we also need to know how gen M is related to gen 0. #C For the P/2 case, gen M can be either a mirror image of gen 0, a 180 #C degree rotation of it, or a 90 degree rotation of it if the pattern #C has 180 degree rotational symmetry. For the P/4 case gen M must be a #C 90 degree rotation of gen 0. In any case, if we merge all gens which #C are multiples of M, the resulting pattern will have more symmetry than #C the original oscillator. We describe the complete symmetry class of #C the oscillator by appending the one or two character description of #C the union's symmetry to that of gen 0's symmetry. For example, if #C gen 0 has 180 degree rotational symmetry about a cell center, and #C gen M is obtained by reflecting gen 0 across a diagonal, then the #C union of gens 0 and M is symmetric across both diagonals, so its #C symmetry class is denoted ".cxc". #C #C The 43 possible symmetry types are: #C #C period/mod = 1: nn -c-c -e-e // .c.c .e.e .k.k +c+c #C +e+e +k+k xcxc xkxk rcrc rkrk *c*c *k*k #C #C period/mod = 2: n-c n-e n/ n.c n.e n.k #C -c+c -c+e -e+e -e+k #C /xc /xk #C .c+c .cxc .crc .e+e .k+k .kxk .krk #C +c*c +k*k xc*c xk*k rc*c rk*k #C #C period/mod = 4: nrc nrk #C #C The collection includes examples of all of these with mod=1, and many #C with larger periods. #C #C ---------------------------------------------------------------------- #C Period 1 oscillators are usually called "still-lifes". Programs #C written by MDN and others have counted the still-lifes with N cells #C for small N; the results up to N=20 are shown here: #C #C N 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 #C # 2 1 5 4 9 10 25 46 121 240 619 1353 3286 7773 19044 45759 112243 #C #C Those with up to 10 bits are included in the stamp collection. So are #C some larger ones that either occur naturally in random soups, or are #C useful, or exemplify symmetry types. I'm omitting the discoverers and #C dates for most of the small and naturally occurring ones, since they've #C been independently discovered many times. #C #C There are 2 4-bit still lifes: #C 1.0.0 "block" [JHC group 1970] Example of "*k" symmetry. Used #C as an eater in many oscillators, such as 4.1.0, 5.2.4, 6.0.0, #C 8.0.0, 10.1.0, 11.0.1, 12.1.1-2, 18.0.0, 28.0.0, 29.0.1, #C 30.0.0, 32.0.1, 44.0.0, 46.0.0, 56.0.0, 124.0.0, 135.0.0, #C 150.0.0, 188.0.0, 246.0.0, 360.0.0, and 460.0.0. Also used as #C a 'rephaser' in 135.0.0, 150.0.0, and 240.0.0. #C 1.0.1 "tub" [JHC group 1970] Example of "*c" symmetry. Used as an #C eater in 12.2.1, 24.0.0, most p29s, 30.2.0-3, and 47.0.0. #C #C There's 1 5-bit still life: #C 1.0.2 "boat" [JHC group 1970] Example of "/" symmetry. #C #C There are 5 6-bit still lifes: #C 1.0.3 "ship" [JHC group 1970] Example of "xc" symmetry. Used as an #C eater of traffic lights in 24.1.0 and 24.2.0. #C 1.0.4 "barge" [JHC group 1970] Example of "xk" symmetry. #C 1.0.5 "snake" [JHC group 1970] Example of ".k" symmetry. Used in #C 60.4.1 and 15240.0.0 to convert a glider into a boat, which a #C subsequent glider deletes. #C 1.0.6 "beehive" [JHC group 1970] Example of "+e" symmetry. This #C often occurs in a group of 4, known as a "honey farm", which #C arises, for example, from a beehive with an extra cell in one #C of its corners. #C 1.0.7 "aircraft carrier". Example of ".e" symmetry. #C #C There are 4 7-bit still lifes: #C 1.0.8 "long boat" [JHC group 1970] #C 1.0.9 "long snake". Example of ".c" symmetry. #C 1.0.10 "loaf" [JHC group 1970] #C 1.0.11 "eater" or "eater1" (formerly "fishhook") [* 1971] Smallest #C asymmetric still-life. This is a very useful still-life, #C because of its ability to eat gliders (e.g. 30.0.1), beehives #C (30.0.2), and lightweight and middleweight spaceships (46.2.0 #C and 46.3.0), and to modify many other things. The term #C "eater" also applies to other still-lifes (and occasionally #C oscillators) that share this ability; the most useful of these #C are the block (1.0.0), eater2 (1.7.3), and eater3 (1.7.4), but #C many others are sometimes useful, including the tub (1.0.1), #C ship (1.0.3), and snake (1.0.5). #C #C There are 9 8-bit still lifes: #C 1.1.0 "long ship" [JHC group 1970] #C 1.1.1 "long barge" [JHC group 1970] #C 1.1.2 "long long snake" #C 1.1.3 "sinking ship" #C 1.1.4 "pond" [JHC group 1970] #C 1.1.5 "shillelagh" [Charles L. Corderman & Hugh Thompson 1971] #C 1.1.6 "tub with tail" [Charles L. Corderman & Hugh Thompson 1971] #C 1.1.7 "hook with tail" #C 1.1.8 "mango" #C #C There are 10 9-bit still lifes. Only 7 have names: #C 1.2.0 "long long boat" #C 1.2.1 "long^3 snake" #C 1.2.2 "long sinking ship" #C 1.2.3 "hat" [* 1971] Example of "-c" symmetry. #C 1.2.4 "integral sign" #C 1.2.5 "up-boat with tail" #C 1.2.6 "down-boat with tail" #C 1.2.7 "long shillelagh" #C 1.2.8-9 unnamed #C #C There are 25 10-bit still lifes. Only 9 have names: #C 1.3.0 "long long ship" #C 1.3.1 "long long barge" #C 1.3.2 "long^4 snake" #C 1.3.3 "long long sinking ship" #C 1.3.4 "snake siamese snake" #C 1.3.5 "snake siamese aircraft carrier" #C 1.3.6 "aircraft carrier siamese aircraft carrier" #C 1.3.7 "long integral" #C 1.3.8-13 unnamed #C 1.4.0 "beehive with tail" #C 1.4.1 "up-barge with tail" #C 1.4.2 "down-barge with tail" #C 1.4.3-6 unnamed #C 1.4.7 "loop" #C 1.4.8 "block and table" #C 1.4.9 "loaf siamese barge" #C 1.4.10 "bi-boat" or "boat-tie" or "bow tie" #C #C Still lifes 1.5.0-10 and 1.6.0-4 are some larger ones that sometimes #C occur in random soups. #C 1.5.0 "bi-ship" or "half fleet" (A "fleet" consists of 2 of these, #C and arises, for example, from a ship with an extra bit added #C at one end.) #C 1.5.1 "bi-loaf" or "half bakery" #C 1.5.2 "paper clip" #C 1.5.3 "big S" [MIT group 1971] #C 1.5.4 "bi-pond" #C 1.5.5 "boat-ship tie" #C 1.5.6 "pair of tables" #C 1.5.7 "moose antlers" #C 1.5.8 "cis-mirrored R-bee" #C 1.5.9 "block on big table" #C 1.5.10 "twin peaks" #C 1.6.0 "dead spark coil" #C 1.6.1 "beehive on big table" #C 1.6.2 "scorpion" Occurs in gens 4760-5165 of "rabbits", this 9-bit #C methuselah found by Andrew Trevorrow: #C o...ooo #C ooo..o. #C .o..... #C 1.6.3 "fourteener" #C 1.6.4 "bookends" #C #C Still lifes 1.6.5-8 and 1.7.0-2 provide examples of other symmetries. #C 1.6.5 Example of "-e" symmetry #C 1.6.6 "beehive with 2 tails" Example of "-e" symmetry #C 1.6.7 Example of "+c" symmetry #C 1.6.8 "spiral" [RTW 1971] Example of "rc" symmetry #C 1.7.0-1 Examples of "+k" symmetry #C 1.7.2 Example of "rk" symmetry. Heinrich Koenig pointed out that there #C are smaller examples; the smallest are: #C ..oo.o.. ...o.o.. #C ..o.oo.. .oooo.o. #C oo....oo o.....o. #C .o.oo..o .o.oo.oo #C o..oo.o. oo.oo.o. #C oo....oo .o.....o #C ..oo.o.. .o.oooo. #C ..o.oo.. ..o.o... #C #C Still lifes 1.7.3-6 are eaters that are used in various oscillators. #C 1.7.3 "eater2" [DJB ????] See 6.3.2, 6.5.2, and 13.0.0. #C 1.7.4 "eater3" [DJB 6/22/77] See 8.2.1, 18.0.0, 42.0.0, 50.0.1, #C 55.0.0, 246.0.0. #C 1.7.5 "eater4" [DJB ????] See 9.0.4, 11.0.2, 29.0.1-2, 29.3.0-1. #C 1.7.6 unnamed eater [DJB ????] I don't know any oscillators that #C use this. Here it's shown deleting a loaf: #C .........o.... #C ...o....o.o... #C ..o.o...o.ooo. #C .o..o..oo....o #C ..oo..o...ooo. #C ......ooooo... #C ....oo........ #C ...o.o..ooo... #C .ooo.o.o..o... #C o....o.o...... #C .oo.oo.oo..... #C ..o.o......... #C ..o.o......... #C ...o.......... #C #C 1.7.7 [DJB 3/78?] Unnamed eater, used in 6.3.3 and 32.0.0. #C #C The 10 digits: [DRH 5/8/92; "4" changed 3/94] #C #C ---------------------------------------------------------------------- #C #C There are 20 known p2 oscillators with <= 14 cells (in gen 0). #C There's 1 with 3 cells: #C 2.0.0 "blinker" [JHC 3/70] Example of "+c*c" symmetry. This #C often occurs in a group of 4, known as a "traffic light", #C which arises, for example, from a T-tetromino. #C #C There are 3 with 6 cells: #C 2.0.1 "toad" [SN 5/70] Note use as an eater ("killer toads") in, #C for example, 4.9.1, 6.2.5, 46.4.0, and 60.5.0. See discussion #C of toad hasslers at 60.0.0. #C 2.0.2 "beacon" [JHC 3/70] #C 2.0.3 "clock" [SN 5/70] Example of ".kxk" symmetry. #C #C For any N>=8, there's at least one p2 with N cells. Generically these #C are called barber poles (see 2.7.0). For 8<=N<=11 these are the only #C known p2s; the first 3 have names: #C 2.0.4 "bipole". Example of ".cxc" symmetry. #C 2.0.5 "tripole". Example of "/xk" symmetry. #C 2.0.6 "quadpole". Example of ".cxc" symmetry. #C #C There are 4 with 12 cells (including the 6-pole, which isn't shown): #C 2.0.7 #C 2.0.8 "the fox" or "gnome" [DJB 7/77] Smallest asymmetric p2. #C 2.0.9 "flip flops" [MIT group 12/71] Example of "rk*k" symmetry. #C #C There are 2 with 13 cells, the 7-pole and: #C 2.0.10 "by flops" [RTW ????] Example of "-c+e" symmetry. #C #C There are 6 with 14 cells, the 8-pole and: #C 2.1.0 #C 2.1.1 #C 2.1.2 "why not" [DJB 7/77] #C 2.1.3 "eater plug" [RTW 2/73] #C 2.1.4 "test tube baby" #C #C Oscillators 2.0.2 (beacon), 2.1.3 (eater plug), and 2.1.4 (test tube #C baby) are examples of on-off oscillators, in which generation 0 is a #C subset of generation 1. Other examples are shown in 2.1.5 to 2.1.9. #C 2.1.5 "spark coil" [* 1971] #C 2.1.6 "4 boats" #C 2.1.7 "light bulb" [* 1971] #C 2.1.8 variant of light bulb #C 2.1.9 "scrubber" [* 1971] #C #C Oscillators 2.1.8 to 2.5.4 provide examples of the remaining p2/2 #C symmetry types. #C 2.2.0 "quad" [Robert A. Kraus 4/71] Example of "rk*k" symmetry. #C 2.2.1 "cloverleaf" [RTW before 6/72] Example of "xc*c" symmetry. #C 2.2.2 "singular flip flop" [RTW 7/72] Example of "n-e" symmetry. #C 2.2.3 "almosymmetric" [* 1971] Example of "n-e" symmetry. #C #C 2.2.4 Example of "-c+e" symmetry. #C 2.2.5 [DRH 5/20/93] Example of "n-c" symmetry. #C 2.2.6 [DRH 4/23/93] Example of ".c+c" symmetry. #C 2.3.0 [DRH 5/20/93] Example of "n/" symmetry. #C 2.3.1 "Laputa" [RCS 9/23/92] Example of "n.e" symmetry. #C 2.3.2 "blinkers bit pole" [RTW 6/77] Example of "n.e" symmetry. #C 2.3.3 [DRH 5/20/93] Example of "n.k" symmetry. #C 2.3.4 [DRH 5/20/93] Example of "n.k" symmetry. #C 2.3.5 [DRH 4/23/93] Example of ".k+k" symmetry. #C 2.3.6 Example of ".kxk" symmetry. #C 2.4.0 "piston" [* 1971] Example of "-c+c" symmetry. #C 2.4.1 Example of "-c+c" symmetry. #C 2.4.2 [DRH 5/20/93] Example of "n.c" symmetry. #C 2.4.3 "complementary blinker" [AF 7/12/94]. Example of ".c+c" #C symmetry. #C 2.4.4 Example of ".cxc" symmetry. #C 2.4.5 [DRH 4/23/93] Example of "/xc" symmetry. #C 2.4.6 [DRH 4/23/93] Example of ".crc" symmetry. #C 2.5.0 [DRH 4/23/93] Example of "rc*c" symmetry. #C 2.5.1 [AF 7/26/94] Example of "rk*k" symmetry. A muttering moat; #C see 2.12.2. #C 2.5.2 [DRH 4/23/93] Example of "xk*k" symmetry. #C 2.5.3 [DRH 1973] Example of "-e+e" symmetry. Infinitely extensible. #C 2.5.4 [DRH 4/23/93] Example of "-e+e" symmetry. #C 2.5.5 [DRH 4/23/93] Example of "-e+e" symmetry. #C 2.5.6 [DRH 4/23/93] Example of "-e+k" symmetry. #C 2.6.0 Example of ".e+e" symmetry. #C 2.6.1 Example of "+k*k" symmetry. #C 2.6.2 Example of "+k*k" symmetry. #C 2.6.3 Example of ".krk" symmetry. #C 2.6.4 Example of "xk*k" symmetry. #C #C Oscillators 2.7.0 to 2.9.1 are examples of stabilized wicks, which may #C be made arbitrarily long. #C 2.7.0 "barber pole" [MIT group 1970] #C 2.7.1 [RTW <1990] #C 2.7.2 [DRH 1994] #C 2.7.3 [RTW <1990] #C 2.7.4 [bottom end: RTW <1990; top end: DRH 1995] #C 2.7.5 [RTW <1990] #C 2.8.0 [DRH 1994] #C 2.8.1 [AWH 8/25/94] This was discovered as a stabilizer for 4.4.1. #C 2.9.0 [DRH 1994] #C 2.9.1 [DRH 1994] #C #C Oscillators 2.10.0 to 2.12.1 are stabilized agars, which may be #C made arbitrarily large. #C 2.10.0 "venetian blinds" [DRH 9/12/92] This uses diagonal edges for #C the agar. A vertical edge is also known, along with a corner #C joining it to the diagonal edge. It's easy to prove that #C horizontal edges don't exist. #C 2.10.1 [DRH 12/4/94, improved by MDN 12/6/94] #C 2.11.0 "houndstooth agar" [DRH 3/30/94] #C 2.11.1 [agar found by Robert A. Kraus 1971, stabilized by DRH 12/13/94] #C 2.11.2 #C 2.12.0 [agar found by Robert A. Kraus 1971, stabilized by ????] #C 2.12.1 "quilt" or "squaredance" [agar found by Don Woods, 1971, stabilized #C by DRH 3/25/93] #C 2.12.2 "ring of fire" [DRH 9/24/92] A "muttering moat"; i.e. an #C oscillator whose rotor consists of a closed loop of cells, #C each of which touches exactly 2 others. Also see 2.5.1. #C ---------------------------------------------------------------------- #C One other p3 is included as part of 12.4.0. #C #C 3.0.0 "caterer" [DRH 8/4/89] Both this and jam (3.0.1) supply a #C spark which is used, e.g., in 3.4.0-3.4.3, 6.5.2, 12.0.2, #C 12.0.3, 12.1.1, and 21.0.0. Also see the multiple caterer #C used in 12.4.0. #C 3.0.1 "jam" [AF 1988] #C 3.0.2 "2 eaters" [RWG 9/71] #C 3.0.3 "eaters plus" [RTW 7/91] #C 3.0.4 "biting off more than they can chew" [Peter Raynham 7/72] #C 3.0.5 "trice Tongs" [RTW 2/82] #C 3.0.6 "pulse" [DJB#46 7/73] #C 3.0.7 "pulsar 18-22-20" [DJB#47 7/73] Two copies of 3.0.6. #C 3.0.8 [RTW 4/82] #C 3.1.0 [DRH 8/89] volatility = 17/18, which was the maximum known #C for a p3 until 3.8.1 was discovered. #C #C Oscillators 3.1.1 to 3.1.3 all have rotors made of 3 cells in a #C triangle, but with different cycles. #C 3.1.1 "cuphook" or "MIT oscillator" [RCS 10/70] #C 3.1.2 "stillater" [RTW 9/85] #C 3.1.3 "1-2-3" [DJB#4 8/72] #C #C 3.1.4 [AF 8/22/94] Rotor consists of 2 copies of that in 3.1.2. #C 3.1.5 "germ" [DJB#9 9/72] #C 3.1.6 [DJB#7 <=1976] Same rotor as in "2 eaters". #C 3.2.0 "period three" [RTW 6/72] Can be reduced by 4 cells, by #C replacing the snakes by joined L tetrominos. #C 3.2.1 "mini pressure cooker" [RTW before 6/72] #C 3.2.2 "pressure cooker" [MIT group 9/71] #C 3.2.3 "hustler" [RTW 6/71] #C 3.2.4 "loading dock" [DJB#3 9/72] #C 3.2.5 "snake dance" [RTW 5/72] #C 3.2.6 "tubber" [RTW before 6/72] Rotor is confined to 2 parallel #C diagonals. Also see 4.2.4. #C 3.3.0 "diamond ring" [DJB#2 1972] #C 3.3.1 "new five" [DRH 1/90] #C 3.3.2 [DJB#92 7/26/76] #C 3.3.3 [DJB#103 6/3/77] Rotor has symmetry type "-c", but stator #C can't be made symmetric. (The left edge can be made 1 column #C narrower and 1 bit smaller by using a block below the snake.) #C 3.3.4 [DRH 10/89] #C 3.3.5 [DJB#79 6/6/76] (DJB found the smallest form of this, with #C just 1 2x3 rectangle. I don't know who found the wick.) #C #C Oscillators 3.4.0-3 are examples of "catered" oscillators. The #C necessary sparks can be supplied by either a caterer (3.0.0) or a #C jam (3.0.1). #C 3.4.0 [DRH 8/89] #C 3.4.1 [DRH 8/89] #C 3.4.2 [RTW 8/89] #C 3.4.3 "skewed traffic light" [RTW 8/89] #C #C 3.4.4 "double ewe" [RTW before 9/71] #C 3.5.0 "double caterer" [DRH 10/89] #C 3.5.1 "triple caterer" [DRH 10/89] Used in 6.6.0. #C 3.5.2 [DRH 1/90] Smallest known p3 in which a corner of the #C bounding box is active. #C 3.5.3 [AF 7/30/94 (symmetric form)] #C 3.5.4 "surprise" [DJB#10 11/72] #C 3.6.0 [DRH 9/10/89] #C 3.6.1 "bent keys" [DRH 8/89] #C 3.6.2 "short keys" [DRH 8/89] This is the shortest version of the #C left wick in 3.6.4. #C 3.6.3 [AF 7/13/94] #C 3.6.4 [left side by DRH 8/89, right side by Charles Trawick 6/71] #C 2 related wicks. The one on the right is "candelabra". The wick #C can also turn a corner, as shown in 3.7.2. #C 3.7.0 "candlefrobra" [RTW 11/84] Variant of "candelabra" (3.6.4). #C 3.7.1 "cross" [RTW 10/89] Same as 3.11.0. One of the few known #C oscillators in which one phase is a polyomino. Also see #C 3.7.2. #C 3.7.2 [HH 2/26/93] A larger version of 3.7.1, which may be made #C any size. #C 3.7.3 "star" [HH 2/16/93] Another polyomino. #C 3.7.4 [HH 3/5/93] Blocks may be added in any of the 4 corners of #C 3.6.3. #C 3.8.0 [DRH 1994] #C 3.8.1 [DRH 11/27/94] Volatility -> 1 as length increases. No #C finite p3 is known with volatility = 1. (Volatility = number #C of rotor cells divided by total number of cells in rotor and #C stator.) #C 3.9.0 [DRH 9/18/89] #C 3.9.1 "p3 rumbling river" [DRH 11/26/94] The rotor is connected #C and contained in a strip of height 2. #C #C In the next 3 rows, each oscillator in the left column consists of #C 4 quarters, which can be rearranged to form larger closed loops #C (middle column) or chains that aren't closed (right column). See #C 5.8.0-5.8.1 for another example. #C 3.10.0 "pulsar" or "pulsar CP 48-56-72" [JHC 3/70] The first #C known, and most commonly occurring, p3 oscillator. #C 3.10.1 "quasar" [RTW 8/71] #C 3.10.2 [???? before 11/27/94] #C 3.11.0 "cross" [RTW 1989] Same as 3.7.1. #C 3.11.1 [DRH 11/27/94] #C 3.11.2 [DRH 11/27/94] #C 3.12.0 [HH 3/5/93] #C 3.12.1 [DIB 3/7/93] #C 3.12.2 [RWG 9/22/94] #C ---------------------------------------------------------------------- #C Some other p4s are included as parts of oscillators with larger #C periods, namely 124.1.0-1 and 188.0.0-1. #C #C 4.0.0 "mold" [AF 1988] Period 4/2, symmetry type "n/". Supplies #C a 1-bit spark that's used, e.g., in 8.3.4, 16.1.1, several #C p28s, 32.1.1, 36.0.1, 36.0.2, 40.0.1, 52.0.1, 88.0.0, #C 100.0.1, and 200.0.0. #C 4.0.1 "mazing" [DJB#45 12/73] Period 4/2, symmetry type "/xk". #C 4.0.2 "monogram" or "JHC" [DRH 8/11/89] Period 4/2, symmetry type #C "+c*c". Supplies a spark that's used in 12.2.0-12.3.1. #C 4.0.3 [DRH 8/89] Period 4/2, symmetry type "/xk". Supplies a spark #C that's used in 4.13.1 and 4.17.1. #C 4.0.4 [DRH before 4/92] #C 4.0.5 [DRH 9/89] Supplies a spark that's used in 12.1.0. #C 4.0.6 "Achim's p4" [DJB#88 1976, AF 1988] DJB found a larger #C form of this, using the same pieces that occur in siesta #C (5.2.3) and sombreros (6.1.1). AF found the smaller version. #C The rotor consists of 2 copies of that in 4.2.6. #C 4.0.7 [DJB#23 <1973?] #C 4.1.0 "eater/block frob" [DJB#51 <=1976] #C 4.1.1 "confused eaters" [DJB#49 before 1973] Period 4/2, symmetry #C type "n/". #C 4.1.2 "pinwheel" [SN 4/70] Period 4/4, symmetry type "nrk". #C 4.1.3 "clock II" Period 4/4, symmetry type "nrk". #C 4.1.4 [DJB#28 before 1973?] Rotor is p4/2, symmetry type "rk*k". #C 4.1.5 "T-nosed p4" [RTW 1989] #C 4.1.6 [DRH 1994] A narrower but longer T-nosed p4 #C #C Oscillators 4.2.0 to 4.2.3 are examples of "babbling brooks", in which #C the rotor consists of a chain of cells, each one adjacent to only 1 or #C 2 others. At the time the collection was built, these were the only #C known babbling brooks with period > 2. I found another on 8/3/97: #C #C .......o........ #C .....ooo....oo.. #C ....o...oo..o... #C .o..o.oo..o.o... #C o.o.o....oo..oo. #C .oo..oo....o.o.o #C ...o.o..oo.o..o. #C ...o..oo...o.... #C ..oo....ooo..... #C ........o....... #C #C (For p2 examples, see 2.0.2, 2.1.3-5, and 2.1.7-8.) #C 4.2.0 [DJB#13 before 1973] Period 4/2, symmetry type "n/". #C 4.2.1 [DJB#15 <1973] #C 4.2.2 [DJB#104 6/3/77] #C 4.2.3 [DRH 11/10/94] #C #C 4.2.4 "wavefront" [DJB#24 <=1976] Rotor is confined to 2 parallel #C diagonals. Also see 3.2.6. #C 4.2.5 "Gray counter" [???? 1971] Also see 4.15.1. #C 4.2.6 [DRH 8/89] Also see 4.0.6. #C 4.3.0 [DRH 8/89] Period 4/2, symmetry type "n-e". #C 4.3.1 [DRH 8/89] Period 4/2, symmetry type "n-e". #C 4.3.2 [DRH 8/89] Period 4/2, symmetry type "n-c". #C 4.3.3 [DRH 3/90] Period 4/2, symmetry type "n/". #C 4.3.4 [DRH 3/90] Period 4/2, symmetry type "n/". #C 4.3.5 [DRH 3/90] Period 4/2, symmetry type "n/". #C 4.3.6 [DJB#21 <1973] #C 4.4.0 "penny lane" [DJB#123 1972] #C 4.4.1 [AF 8/22/94 (symmetric form), AWH 8/25/94 (using 2.8.1 for #C right half), DRH 11/23/94 (this p2 on right)] Only 3 cells #C are p4; the rest are p1 or p2. #C 4.4.2 [DJB#98 4/28/77] Period 4/2, symmetry type "n-e". #C 4.4.3 [RTW 1989] #C 4.4.4 [DJB#20 <1977] #C 4.5.0 "windmill" [DRH 11/89] #C 4.5.1 [AF 8/23/94 (symmetric form)] #C 4.5.2 [AF 7/17/94 (symmetric form), RWG,AWH 11/20/94] #C 4.5.3 [AF 8/31/94 (symmetric form)] #C 4.5.4 "boss" [DJB#30 1972] #C 4.5.5 [DJB#69 <=1976] #C #C In 4.6.0 to 4.6.5, only 2 cells are p4; the rest are p1 or p2. #C 4.6.0 [DRH 12/10/94] #C 4.6.1 [RTW 11/90] #C 4.6.2 [DRH 12/10/94] #C 4.6.3 [DRH 12/10/94] #C 4.6.4 [DRH 12/10/94] #C 4.6.5 [DRH 12/10/94] #C #C Oscillators 4.7.0 to 4.10.1 are all related. They are based on this #C infinite oscillator, in which a single row of cells is surrounded by #C 2 lines of blocks (or other things): #C #C oo..oo..oo.oo.oo.oo.o..oo #C oo..oo..oo.oo.oo.o.oo..oo #C ......................... #C ......................... #C ......................... #C ......................... #C ... ooooooooooooooooooooooooo ... #C ......................... #C ......................... #C oo.oo.o..oo.oo.oo..oo..oo #C o.oo.oo..oo.oo.oo..oo..oo #C #C This can be made finite in several ways. First, any of 3 small pieces #C can be attached to the ends. The first is shown in row 4.7. (Also #C see 8.0.5.) The others are shown in 4.8.1 to 4.8.3. (A much larger #C end piece is shown in 4.12.2.) Next, the line can be bent to form a #C corner, as in 4.8.4. If it's bent 4 times, it can form an octagon, #C as in 4.9.0 to 4.10.0. #C #C 4.7.0 "lightweight emulator" [RTW 6/80] #C 4.7.1 "middleweight emulator" [RTW 6/80] Supplies a 1-bit spark #C that's used, e.g., in 20.0.0-20.0.2, 24.1.2, 60.5.1, and #C 124.1.0. #C 4.7.2 "heavyweight emulator" [RTW 6/80] Supplies a domino spark #C that's used, e.g., in 8.3.3, 12.0.2, 12.4.0, 32.0.2, 36.1.2, #C and 44.0.0. #C 4.7.3 "overweight emulator" [RTW ????] #C 4.7.4 #C 4.8.0 [AF 7/13/94] May be compressed horizontally by 1 or 2 cells. #C Also see 4.8.1 and 4.8.3-4. #C 4.8.1 [DRH 7/14/94] Half of 4.8.0, supported by 2 clocks. (This #C use of a clock was discovered, in another universe, by DIB.) #C 4.8.2 [DRH 12/6/94] #C 4.8.3 #C 4.8.4 #C 4.9.0 [RTW ????, AF 8/7/94] An octagon of side 2, showing 2 ways to #C stabilize the edge. #C 4.9.1 [DRH 9/89] An octagon of side 3, showing 4 ways to stabilize #C the edge. #C 4.9.2 "octagon IV" [RTW 1/79] An octagon of side 4. The edges #C can also be stabilized using eaters or toads as in 4.9.1. #C This also works if a block is added in the center. #C 4.9.3 [DRH,RTW 9/89, AF 8/7/94] An octagon of side 5, showing 4 ways #C to stabilize the edge. #C 4.10.0 [AF,DRH 1994] A larger octagon. The corners can also be #C stabilized using eaters or toads as in 4.9.1. #C 4.10.1 [DRH 9/16/92] Stabilized p4 agar, made of several parallel #C lines. #C #C 4.10.2 [DRH ????] Period 4/2, symmetry type "+k*k". #C 4.10.3 [RTW before 10/92] The MW emulators (4.7.1) can be replaced by #C molds (4.0.0). #C #C Pattern 4.7.1 (MW emulator) is often useful because of its 1-bit #C spark. But in some applications the object being sparked would #C collide with the rest of the emulator. In such situations the #C oscillators below may be more useful. (Also see the p4 at the top #C of 124.1.0 and the one in 188.0.0.) #C 4.11.0 [DRH 1994] #C 4.11.1 "fountain" [DRH 11/28/94] Supplies a spark that's used in #C 24.1.0-24.2.1, 124.0.0-1, and 124.1.1. It can also be used #C (not shown) to double the period of a period 4N+2 MWSS stream, #C in a manner similar to that used in 60.5.1 to double the #C period of a LWSS stream. #C 4.11.2 [DRH 1994] #C #C 4.11.3 [AWH 2/10/95] #C 4.11.4 [DRH 4/6/92] #C #C Pattern 4.7.2 (HW emulator) has a useful 2-bit spark. But sometimes #C these are better: #C 4.12.0 [DRH >=11/30/94] Supplies a spark that's used in 12.0.3, #C 60.3.1, and 124.1.1. It can also be used (not shown) to #C double the period of a period 4N+2 HWSS stream, in a manner #C similar to that used in 60.5.1 to double the period of a #C LWSS stream. #C 4.12.1 [DIB,DRH 12/12/94] A longer but narrower version of 4.12.0. #C 4.12.2 [DRH 1994] #C #C 4.12.3 [RTW 9/91, DRH 1/14/95] First stabilization (not shown here) #C was found by RTW 9/91. #C #C 4.13.0 "sixty nine" [RTW 10/78] Period 4/4, symmetry type "nrk". #C #C 4.13.1 [RTW 9/89] Period 4/2, symmetry type ".crc". #C 4.13.2 [DRH 1/10/95] Period 4/4, symmetry type "nrc". #C 4.13.3 [DRH 1/10/95] Period 4/4, symmetry type "nrc". #C 4.14.0 [DRH 10/89] 2 related wicks. The one on the left is #C "turning toads"; it's related to the toad hasslers such as #C 60.1.0 - 60.1.4. #C 4.14.1 [DRH 8/89, AF 1994] #C 4.15.0 #C 4.15.1 [???? 1971] #C 4.16.0 [RTW 9/91] #C 4.16.1 [DRH ????, DIB 12/11/94] #C 4.17.0 [RWG 9/17/94 (wick), 11/20/94 (ends)] The repeating part of #C this wick may be attached to itself in 6 different ways. #C 4.17.1 [RTW 9/89] #C ---------------------------------------------------------------------- #C 5.0.0 "fumarole" [DRH 9/3/89] Supplies a domino spark that's used #C in traffic jam oscillators such as 50.0.0, 100.0.1, 110.0.0, #C 200.0.0. (The domino spark in a HW volcano (5.7.1) is more #C usable.) #C 5.0.1 "octagon II" [Sol Goodman & Arthur C. Taber 1971] #C 5.0.2 [AF 7/13/94] Also see 5.0.3. #C 5.0.3 [AWH 11/19/94] Skewed version of 5.0.2. #C 5.0.4 "pseudo barberpole" [AF 8/22/94] #C 5.0.5 [RTW 1/82, DJB#145 8/15/84] #C 5.0.6 [AF 7/27/94] #C 5.1.0 "technician finished product" [DJB#33 1/73] Also see 5.3.3. #C 5.1.1 "mathematician" [DJB#34 1972] #C 5.1.2 "aVerage" [DJB#35 1973] #C 5.1.3 [DJB#160 1/6/87] #C 5.1.4 [DJB#163 2/19/87] #C 5.1.5 [RTW 1/82 (DJB#146)] #C 5.1.6 "pentant" [DJB#85 7/11/76] #C 5.2.0 "toaster" [DRH 4/1/92] Supplies sparks that are used #C in 15.1.1. #C 5.2.1 "middleweight volcano" or "MW volcano" [DRH 4/6/92] Supplies #C sparks that are used in 10.0.3, 10.1.1, 15.1.1, 20.0.0, #C 20.0.2, all known p25s, 50.0.1, 80.0.0, 230.0.0, and 230.0.1. #C 5.2.2 "101" [AF 8/19/94] #C 5.2.3 "siesta" [DJB#57 1973] Also see 4.0.6, 6.1.1-6.1.4, and #C 8.3.0. #C 5.2.4 [DJB#158 2/25/85] #C 5.2.5 [DJB#101 5/22/77] #C 5.3.0 "chemist" [DJB#38 1973] #C 5.3.1 [DJB#84 7/76?] #C 5.3.2 [DJB#44 ????] #C 5.3.3 "pedestle" [DJB#39 1973] Rotor consists of 2 copies of #C the rotor in 5.1.0. #C 5.3.4 [DRH 1994] 2 fumaroles hassle a long barge. Based on 8.3.1. #C A different mechanism is used in 15.1.0. #C 5.4.0 [DJB#151 9/29/84] #C 5.4.1 [DJB#114 6/21/77] Also see 7.1.2 and 11.0.0. #C #C The next 2 are almost "period 5/2" oscillators: In each one, the top #C and bottom halves go through the same cycle, 2 gens out of phase. #C 5.4.2 [DJB#87 7/15/76] #C 5.4.3 [DJB#142 5/21/84] #C #C 5.4.4 [DRH 10/4/89] #C 5.5.0 "pentoad" [RWG 6/77] Also see 5.5.1 and 6.4.0. #C 5.5.1 "multiple pentoads" [RWG & Scott Kim ????] #C 5.5.2 [DJB#93 7/26/76] #C 5.5.3 [DJB#152 9/29/84] Also see 6.4.2. #C 5.5.4 [AF 8/7/94 (symmetric form), AWH 11/19/94] #C 5.6.0 "electric fence" [HH 10/20/92, DRH 11/23/92, 2/21/93] A #C stream of 'ants' moves leftward from the 'source' at the #C right to the 'sink' at the left. HH found a source that #C moves right at c/4, but no moving sink has been found. DRH #C found the stationary sink and later found the stationary #C source. Also see 5.7.0. #C 5.6.1 [DRH ????] There are 6 adjacent columns with only 1 active #C cell each. #C 5.7.0 "another electric fence" [DRH 1/26/95] Also see 5.6.0. #C 5.7.1 "heavyweight volcano" or "HW volcano" [DRH 2/5/95] Supplies #C sparks that are used in 10.0.3, 10.1.1, 30.4.0, 30.5.0, and #C 35.0.0. #C 5.8.0 "harbor" (so-named because gen 3 consists of 4 ships and #C 8 boats) [DJB#122 9/17/78] #C 5.8.1 [DRH 12/2/94] The pieces of harbor (5.8.0) can be #C rearranged in the same way as 3.10.0-3.12.2. #C ---------------------------------------------------------------------- #C Also see the p6 used in 18.0.1. #C #C 6.0.0 "unix" [DJB#48 2/10/76] Produces a 1-bit spark that's used #C in many oscillators. #C 6.0.1 "A for all" [DRH 3/6/93] #C 6.0.2 [AF 7/25/94] #C 6.0.3 "$rats" [DJB#36 1972] #C 6.0.4 "extremely impressive" [DJB#78 8/76] #C 6.0.5 [DJB#100 5/21/77] #C 6.0.6 [DJB#65 <=1976] #C 6.1.0 [AF 8/7/94 (symmetric form)] Note similarity to unix (6.0.0). #C #C The next 4 oscillators are closely related. Also see 4.0.6, 5.2.3, #C and 8.3.0. #C 6.1.1 "sombreros" [DJB#56 1972] #C 6.1.2 [DJB#133 11/16/80] Also see 6.1.1 #C 6.1.3 [DJB#58 <=1976] #C 6.1.4 [DJB#59 <=1976] #C #C 6.2.0 [DRH 8/89] Period 6/2, symmetry type ".e+e". #C 6.2.1 [DRH 8/89] Period 6/2, symmetry type ".e+e". #C 6.2.2 [AF 7/13/94] #C 6.2.3 [DJB#72 <=1976] #C 6.2.4 [DJB#102 6/3/77] #C 6.2.5 [RTW 1989] Also see 6.2.6. #C 6.2.6 [DJB#141 4/25/84] Also see 6.2.5. #C 6.3.0 [DRH 8/89] Period 6/2, symmetry type "n/". #C 6.3.1 [AF 7/26/94] #C 6.3.2 [DJB#132 10/30/80] #C 6.3.3 [DJB#117 9/1/77] #C 6.3.4 [DJB#121 3/4/78] Also see 32.0.0. #C 6.3.5 [DJB#110 6/19/77] #C 6.4.0 [DJB#99 5/12/77] Also see 5.5.0. #C 6.4.1 "trivial p6" [DRH 12/10/94] There are no period 6 cells; #C the left 7 columns are p2; the rest are p3. #C 6.4.2 [DJB#157 10/14/84] Also see 5.5.3. #C 6.4.3 [DRH 9/22/94] #C 6.5.0 "symmetric T-nosed p6" [AF 8/31/94] #C 6.5.1 "T-nosed p6" [AF 9/12/94] Supplies a spark that's used in #C 12.4.1. #C 6.5.2 [DRH 9/89] Period 6/2, symmetry type "-e+e". #C 6.5.3 [RTW 11/16/94] 4 unixes support a simple diagonal wick. #C 6.6.0 [right end:RTW 10/78, middle and left end:DRH 10/89] #C 6.7.0 [NDE 11/21/94] The wick (left end) was found by AF (8/19/94); #C NDE stabilized it; the variations are by DRH (11/22&27/94). #C 6.8.0 [wick by DJB 1973, ends by DRH 1995?] #C ---------------------------------------------------------------------- #C 7.0.0 "burloaferimeter" [DJB#40 1972] Also see 7.0.1. #C 7.0.1 "airforce" [DJB#41 1972] Rotor consists of 2 copies of #C the rotor in burloaferimeter (7.0.0). #C 7.0.2 [DJB#77 <=1976] #C 7.0.3 [DJB#106 6/6/77] Right half can also be turned upside-down #C and shifted up 2 units. #C 7.0.4 [DJB#109 6/19/77] Supplies a domino spark that's used in #C 21.0.0, 105.0.0, and 329.0.0. Also see 26.1.0, where an #C equivalent p7 gets phase-shifted by 2 gens. #C 7.1.0 [DRH 9/22/94] #C 7.1.1 [DRH 10/1/94] #C 7.1.2 [DJB#113 6/21/77] Also see 5.4.1 and 11.0.0. #C 7.1.3 [DJB#135 9/7/81] #C ---------------------------------------------------------------------- #C 8.0.0 "blocker" [RTW ????] Supplies a spark used in 16.0.1, 16.1.1-2, #C 24.1.3, 40.0.1, 72.0.0, and 360.0.0. #C 8.0.1 "Kok's galaxy" [Jan Kok 1971] Supplies a spark used in 56.0.0, #C 120.3.0, 128.0.0, and 856.0.0. #C 8.0.2 "figure 8" or "big beacon" [SN 1970] Supplies sparks used #C in 8.3.1-2, 8.5.0-2, 16.0.2, 24.1.1, 24.2.1, 32.1.1, 40.0.1, #C 40.1.0, 96.0.0, 120.3.0, 128.0.0, and 808.0.0. #C 8.0.3 "smiley" [AF 7/17/94] #C 8.0.4 [AF 7/20/94] Period 8/2, symmetry type ".cxc". #C 8.0.5 [DRH 11/16/94] A p8 variant of the p4 emulators; see #C 4.7.0-4.7.3. #C 8.1.0 "cauldron" or "crucible" [Don Woods, RTW 1971] #C 8.1.1 "Hertz oscillator" [JHC group 1970] #C 8.1.2 "R2D2" [Peter Raynham early 1970s (with a different stator), #C redeiscovered and named by NDE 8/14/94] #C 8.1.3 "pyrotechnecium" [DJB#42 1972] (This was mis-named #C "pyrotechneczum" for many years.) #C 8.1.4 [AF 8/26/94] Supplies a 2-bit spark, which might be usable #C when the one in figure 8 (8.0.2) fails. #C 8.1.5 [DJB#80 6/30/76] #C 8.2.0 [RTW 1989] #C 8.2.1 [DJB#115 6/22/77] #C 8.2.2 "roteightor" [RTW 1972] Also see 8.2.3. #C 8.2.3 "multiple roteightors" [DRH 1/90] A finite agar of any size #C can be constructed in this way. #C 8.2.4 [DJB#105 6/6/77] #C 8.3.0 [DJB#55 <=1976] #C 8.3.1 [RTW 9/84] 2 figure 8s hassle a long barge. Also see 5.3.4. #C A different mechanism is used in 15.1.0. #C 8.3.2 [AF 8/31/94] 4 figure 8s hassle a tub. #C 8.3.3 "p8, type 0 toad flipper" See discussion at 60.0.0. #C 8.3.4 [RTW 9/89] Period 8/2, symmetry type "/xk". #C #C The next 3 are closely related: #C 8.4.0 [DJB#90 7/16/76] #C 8.4.1 [DJB#138 1/23/83] #C 8.4.2 [DJB#94 7/29/76] #C #C 8.4.3 "bottle" [AF 8/7/94] Also see "ship in a bottle", 16.0.1. #C 8.5.0 "tumbling T-tetson" [RTW ????] #C 8.5.1 [DJB ????] "nonstandard type 1 p8 toad sucker" See #C discussion at 60.0.0. #C 8.5.2 [DJB ????] "nonstandard type 2 p8 toad flipper" See #C discussion at 60.0.0. #C ---------------------------------------------------------------------- #C 9.0.0 "worker bee" [DJB#52 1972] #C 9.0.1 multiple worker bees #C 9.0.2 [DJB#43 1972??] #C 9.0.3 [DJB#83 7/10/76] #C 9.0.4 [DJB#155 10/9/84] #C 9.1.0 "snacker" [MDN 1972] #C 9.1.1 multiple snackers #C 9.1.2 [RWG 7/15/94] Based on 15.0.1. #C 9.1.3 [RWG 7/15/94] Based on 15.0.2. #C ---------------------------------------------------------------------- #C 10.0.0 [DJB#76 <=1976] #C 10.0.1 [DJB#161 1/21/86] #C 10.0.2 [DJB#153 9/30/84] #C 10.0.3 [DRH 2/16/95] 2 p5s hassle a blinker. Also see 10.1.1. #C 10.1.0 [DJB#139 5/1/83] #C 10.1.1 [DRH 2/16/95] 4 p5s hassle a blinker. Also see 10.0.3. #C ---------------------------------------------------------------------- #C 11.0.0 [DJB#112 6/20/77] Also see 5.4.1 and 7.1.2. #C 11.0.1 [AF 8/4/94] #C 11.0.2 [DJB#156 10/9/84] #C ---------------------------------------------------------------------- #C 12.0.0 "dinner table" [RTW 1972] Period 12/4, symmetry type "nrc". #C 12.0.1 [DJB#159 1986?] #C 12.0.2 [NDE 1/3/95] Supplies a spark that's used in 24.0.1, #C 48.0.0, 96.0.0, 132.0.0, 144.1.0, and 156.0.0. It should #C also be used in 36.1.2, but an earlier version of the p12 #C was inadvertently used there. Also see 12.4.0. #C 12.0.3 [DRH 1/4/95] A larger version of 12.0.2, with a more #C accessible spark. #C 12.1.0 [AF,AWH,RWG 8/8/94] First found on a 32x32 torus, without #C the outer p4s. #C 12.1.1 "baker's dozen" [RTW 8/89] Earlier versions used sparks #C from p4 and p6 oscillators. #C 12.1.2 [DJB#131 10/26/80] 4 baker's dozens, using only stable #C objects and each other for support. #C #C Oscillators 12.2.0 to 12.3.1 are variations on a p12 wick. #C 12.2.0 #C 12.2.1 [DJB <1980, RTW 1989] Originally supported by MW emulators; #C RTW found that monogram works too. #C 12.3.0 #C 12.3.1 "carnival shuttle" [RTW 9/84] Originally used MW emulators #C at the ends. ???? {see RTW's 11/10/89 ltr} #C 12.4.0 [MDN, DRH >~2/20/95] A wick based on 12.0.2, using a p3 #C multiple caterer. #C 12.4.1 [NDE 6/9/95] #C ---------------------------------------------------------------------- #C 13.0.0 [DJB#96 7/31/76] #C ---------------------------------------------------------------------- #C 14.0.0 "tumbler" [George Collins, Jr. 1970] Period 14/2, symmetry #C type "-c+c". #C ---------------------------------------------------------------------- #C 15.0.0 "pentadecathlon" or "PD" [JHC 1970] Supplies sparks used in #C ???? {mention phase changers} #C 15.0.1 [RTW 10/78] 2 PDs hassle 2 blocks symmetrically. Also see #C 9.1.2. #C 15.0.2 "Jolson" [RTW 11/84] 2 PDs hassle 2 blocks asymmetrically. #C 15.0.3 [DJB 3/73] 4 PDs hassle 4 blocks. #C 15.1.0 [DJB 7/73] 2 PDs hassle a long barge. Note that this is #C not the same mechanism as in 5.3.4 and 8.3.1. #C 15.1.1 "p15 biblock hassler" [DRH 2/21/95] See description #C at 16.1.1. #C 15.1.2 "loaflipflop" [RTW 1990] 4 PDs hassle a loaf. #C ---------------------------------------------------------------------- #C 16.0.0 [AF 7/27/94] Period 16/2, symmetry type "rc*c". #C 16.0.1 "2 pre L hassler" [RTW 7/83] 4 blockers hassle a pair of #C pre-loafs. Period 16/2, symmetry type ".k+k". #C 16.0.2 "sailboat" [RTW 6/84] The 2 p8 oscillators (figure 8 and #C Kok's galaxy) supply sparks which attack the boat in the #C same way, but it's not possible to use 2 copies of either. #C 16.1.0 "ship in a bottle" [RWG 8/7/94] Period 16/2, symmetry #C type "/xk". #C 16.1.1 "p16 biblock hassler" [NDE 2/20/95] 2 1-bit sparks (from #C a blocker (8.0.0) and a mold (4.0.0)) hassle a pair of #C blocks. Sparks can also come from oscillators of period 5 #C (see 15.1.1), 6 (see 18.1.0), 12, 29, 47, or 72 (not shown). #C The biblock creates a 1-bit spark of its own in gen 13, so #C it's possible to build a loop of 4 of them (see 52.0.1). #C Also see 16.1.2 for a symmetric version. #C 16.1.2 "symmetric p16 biblock hassler" [NDE 2/21/95] See #C description at 16.1.1. #C 16.2.0 [AF 8/7/94 (on a 32x32 torus), RWG 8/17/94] #C 16.2.1 [RWG 8/9/94 (ship inside), RWG 8/17/94 (toad hassler)] #C A nonstandard toadflipper; see discussion at 60.0.0. #C ---------------------------------------------------------------------- #C 18.0.0 [DJB before 5/91] Period 18/2, symmetry type "n.e". #C 18.0.1 [DRH 1/1/95] 2-glider shuttle. See comments for 42.0.0. #C 18.1.0 "p18 biblock hassler" [NDE 2/20/95] See description #C at 16.1.1. #C ---------------------------------------------------------------------- #C 20.0.0 [NDE 3/22/95] A period 9+11 traffic light hassler. #C 20.0.1 [NDE 4/2/95] A period 10+10 traffic light hassler. #C 20.0.2 [NDE 6/29/95] Sparks from some p4 and p5 oscillators #C hassle a loaf. #C ---------------------------------------------------------------------- #C 21.0.0 [RTW 2/21/95] A period 10+11 traffic light hassler. #C ---------------------------------------------------------------------- #C 24.0.0 "p24, type 2 toadflipper" [RWG 1994] See discussion at 60.0.0. #C 24.0.1 [NDE 11/20/94] #C 24.1.0 [RWG 11/29/94] #C 24.1.1 [RWG 11/29/94] MDN found (not shown; 11/30/94) that an #C eater can be added at the top left in gen 14 to produce a #C rather inaccessible 1-bit spark. #C 24.1.2 [RWG 11/29/94] #C 24.1.3 [NDE 11/29/94] #C 24.2.0 [RTW 12/10/94] Produces a 2-bit spark that's used in #C 2 p48 toad hasslers (48.0.1-2). Also see 24.2.1. #C 24.2.1 [RWG 12/12/94] A variant of 24.2.0. #C ---------------------------------------------------------------------- #C All known p25 oscillators are based on pushing 2 or more traffic light #C predecessors 3 units in 14 gens and pushing them back in 11 gens. #C No way is known to do this with just one pre-t.l. #C 25.0.0 [NDE 9/23/94 (with toasters instead of eaters), DRH 10/19/94] #C 25.0.1 [NDE 11/5/94] #C 25.1.0 [NDE 11/5/94] #C 25.1.1 [NDE 11/18/94] #C 25.2.0 [NDE 11/18/94] #C ---------------------------------------------------------------------- #C 26.0.0 [DJB#140 1/18/83] #C 26.0.1 #C 26.1.0 [use of p7s in top by RWG 8/24/94; see RWG 10/30/94] #C ---------------------------------------------------------------------- #C All known p28 and p29 oscillators are "pulsar hasslers". Consider a #C pair of hollow 3x3 squares, with 3 empty columns between them: #C ooo...ooo #C o.o...o.o #C ooo...ooo #C After 15 generations, this becomes 4 hollow squares: #C ooo...ooo #C o.o...o.o #C ooo...ooo #C ......... #C ......... #C ......... #C ooo...ooo #C o.o...o.o #C ooo...ooo #C (This goes on to become a p3 "pulsar" in gen 20.) By repeatedly #C suppressing 2 of the hollow squares, we obtain oscillators of #C periods 30 and 60; see 30.2.0-3 and 60.5.0. #C #C It's also possible to suppress 2 of the squares in such a way that #C the other 2 form in gen 14 instead of 15; this leads to oscillators #C with periods 28 and 29. Originally this required 8 pairs of squares #C supporting each other; DJB found the first p28 ("newshuttle", not #C included in this collection) in 1973. Later, several methods were #C found which use either 1, 2, or 4 mutually supporting pairs. #C #C 28.0.0 #C 28.0.1 #C 28.0.2 #C 28.0.3 [RWG 7/31/94] #C 28.1.0 #C 28.1.1 #C 28.1.2 "smaller newshuttle" [DJB#64 8/2/80] #C 28.2.0 #C 28.2.1 #C 28.2.2 #C ---------------------------------------------------------------------- #C 29.0.0 #C 29.0.1 #C 29.0.2 #C 29.1.0 #C 29.1.1 #C 29.1.2 #C 29.2.0 [RWG 7/31/94] #C 29.2.1 "prime" [DJB#127 8/2/80] #C 29.2.2 #C 29.3.0 "p29 PD hassler" [RWG ????, DRH 12/13/94] 2 copies of #C 29.0.1 change the phase of a PD. Supplies a 2-bit spark #C that's used in 58.0.0. Also see 36.1.0 and 54.1.0. #C 29.3.1 #C 29.3.2 #C ---------------------------------------------------------------------- #C 30.0.0 "queen bee" or "p30 shuttle" [RWG 1970] The central #C part (the shuttle) reappears, reflected across a vertical #C line, in 15 gens, but a beehive is also produced, which #C would destroy the shuttle. The beehive can be destroyed #C by a block, as shown here, or by an eater in one of two #C different positions, as in 30.0.2. #C 30.0.1 "p30 glider gun" [RWG 11/70] #C 30.0.2 2 p30 shuttles push a beehive back and forth. This also #C demonstrates the 2 positions of an eater that stabilize #C the shuttle. #C 30.1.0 [NDE 10/30/94] 2 p30 shuttles repeatedly change the phase #C of a blinker. #C 30.1.1 [DIB 9/1/92] 2 p30 shuttles repeatedly reverse a loaf. #C 30.1.2 [RTW ????] 2 p30 shuttles repeatedly convert blocks to #C gliders. Also see 92.3.0. #C 30.2.0 "Eureka" [DJB#130 8/16/80] The simplest pulsar hassler. #C Can also be skewed, by moving one half up 2 units. #C 30.2.1 #C 30.2.2 #C 30.2.3 "pulshuttle V" [RTW 5/85] #C 30.3.0 "hectic" [RTW 9/84] Period 30/2, symmetry type ".crc". #C 30.3.1 "p30 LWSS gun" #C 30.4.0 [DRH 2/14/95] 4 p5s hassle a beehive. Also see 35.0.0. #C 30.4.1 [????] 6 gliders in a 180 gen loop. This use of a queen bee #C as a reflector is called a "buckaroo". #C 30.5.0 "zweiback" [MDN 2/13/95] #C ---------------------------------------------------------------------- #C 32.0.0 "gourmet" [DJB#120 3/4/78] Period 32/4, symmetry type #C "nrk". Also see 6.3.4. #C 32.0.1 "popover" [RTW 8/84] Period 32/4, symmetry type "nrk". #C 32.0.2 "pi portraitor" [RTW 1984 or 1985] Period 32/4, symmetry #C type "nrk" #C 32.1.0 [RTW 5/85] Period 32/2, symmetry type "n.c". Two gourmets #C overlap, sharing a loaf. It's possible to build an #C arbitrarily large agar this way. #C 32.1.1 [NDE 1/26/95] Period 32/2, symmetry type "-c+e". #C ---------------------------------------------------------------------- #C 35.0.0 [DRH 2/14/95] 4 p5s hassle a beehive. Also see 30.4.0. #C ---------------------------------------------------------------------- #C 36.0.0 [NDE 1/29/95] #C 36.0.1 "p36 traffic jam" [RWG 10/14/94] #C 36.0.2 [NDE 11/23/94] 2 copies of 36.0.1 change the phase of a PD. #C Also see 29.3.0 and 54.1.0. #C 36.1.0 "p36, type 0 toadflipper" [????] See discussion at 60.0.0. #C 36.1.1 "p36, type 1 toadsucker" [????] See discussion at 60.0.0. #C 36.1.2 [NDE 11/20/94] Could be made smaller using jams instead of #C T-nosed p4s. #C ---------------------------------------------------------------------- #C 40.0.0 [DJB before 5/91] #C 40.0.1 "p40 traffic jam" [NDE 10/14/94] #C 40.1.0 [DRH 11/4/94] A period 20+20 traffic light hassler. Period #C 40/2, symmetry type "-c+e". This use of a bookend as an #C eater also occurs in 25.0.1-25.2.0. #C ---------------------------------------------------------------------- #C 42.0.0 [RTW 9/84, MDN ??/94] A 2-glider shuttle, using a reaction #C in which an eater3 and sparks from 2 unixes reflect a pair of #C gliders. RTW found a period 66+24n version of this; MDN #C noticed that period 42 could be achieved by rearranging the #C unixes. The unixes can also be replaced by period 5 or 47 #C oscillators, giving periods 50+40n (see 50.0.1) and 282+376n #C (see 282.0.0), or by a larger p6 oscillator, giving period #C 18 (see 18.0.1). Also, by a lucky coincidence, the spacing #C between the gliders allows 2 pairs of gliders to cross using #C rephasers, giving periods 246+24n (see 246.0.0), 230+40n #C (see 230.0.0), and 846+376n (not shown). #C ---------------------------------------------------------------------- #C 44.0.0 [DJB 4/2/92] (OBSOLETE: About 4/29/96, NDE found a simpler #C version: Advance the MW emulators 3 gens and delete the 2 #C blocks closest to them.) #C 44.0.1 "p44 glider gun" [DJB 4/2/92] Large sparks from 2 p44 #C oscillators combine to produce gliders. (OBSOLETE: In 10/96, #C DJB found a p44 gun using only 1 p44 oscillator.) #C ---------------------------------------------------------------------- #C 45.0.0 A p15 PD (15.0.0) and a p9 snacker (9.1.0) interact almost #C trivially. #C ---------------------------------------------------------------------- #C Period 46: The p46 shuttle, known as "twin bees", was discovered in #C 1971 by Bill Gosper. Each end of the shuttle can be stabilized by #C either 1 or 2 blocks, as shown in 46.0.0. If only 1 block is used, #C a large spark is produced which can reflect gliders and spaceships #C in several ways. Two shuttles can be combined in at least 5 ways to #C produce glider guns (46.1.0, 46.1.1, 46.2.0, 46.3.0, and the right #C half of 92.4.0). Also see periods 92, 138, 184, 230, 276, 460, 552, #C 690, and 40894. #C #C 46.0.0 "twin bees" or "p46 shuttle" [RWG 1971] #C 46.0.1 [????, DRH 10/26/94] 2 shuttles push a beehive back and forth #C using 2 different reactions. Also see 92.0.0. #C 46.1.0 [RWG ???? {before 3/92}] A p46 glider gun #C 46.1.1 [RWG ???? {before 12/30/90}] Double-barreled p46 glider gun #C 46.2.0 [PC 6/24/94] A p46 glider gun. This one is useful for #C creating gliders parallel to an existing glider stream, #C as in 46.4.0. #C 46.2.1 [RWG <=1992] p46 LWSS gun, based on a 135 degree glider -> #C LWSS reflection. #C 46.3.0 "newgun" [RWG 1971] The first known p46 gun. #C 46.3.1 [RWG <=1992] p46 MWSS gun, based on a 135 degree glider -> #C MWSS reflection from a pair of p46 shuttles. (This glider + #C pre-block -> MWSS reaction is very useful; see 60.6.0 and #C 120.2.0.) #C 46.4.0 [DJB ????, DRH 12/31/90?] p46 HWSS gun. DJB found the only #C known 3-glider synthesis of a HWSS. #C 46.5.0 [DJB? ????] Pseudo p23 gun. The outputs of 2 p46 guns are #C interleaved to produce a p23 glider stream. (Also see #C 60.6.0.) #C 46.5.1 [PC,DRH 1994] p46 glider gun based on a 90 degree #C reflection that changes 1 glider to 2. Also see 230.1.0. #C 46.6.0 "p46 LWSS loop" [Peter Rott 11/93, PC 1994] Based on a #C 90 degree LWSS reflection. #C ---------------------------------------------------------------------- #C 47.0.0 [DJB#137 12/5/82] #C 47.0.1 [???? before 9/92 (horizontal stacking), RWG before 9/92 (skewed #C vertical stacking)] It's possible to build an arbitrarily #C large agar this way. #C ---------------------------------------------------------------------- #C 48.0.0 [RTW 1995] Sparks from 2 p12s move a pair of beehives. #C 48.0.1 "p48, type 2 toadflipper" [RWG 12/11/94] See discussion at #C 60.0.0. #C 48.0.2 "p48, type 2 toadsucker" [RWG 12/11/94] See discussion at #C 60.0.0. #C ---------------------------------------------------------------------- #C 50.0.0 "p50 traffic jam" [NDE 10/16/94] Period 50/2, symmetry #C type "n-e". #C 50.0.1 [DRH 3/19/92 (using early version of toaster)] 2-glider #C shuttle with period 50+40n. See comments for 42.0.0. #C ---------------------------------------------------------------------- #C 52.0.0 [DJB#119 10/1/77] Period 52/4, symmetry type "nrc". #C 52.0.1 [NDE 2/21/95] Period 52/4, symmetry type "nrk". See #C description at 16.1.1. One can also have two pulses #C traveling around the loop separated by 16, 20, or 24 gens, #C or three pulses separated by 16+16+20. #C #C ---------------------------------------------------------------------- #C 54.0.0 [DJB#62 <=1976] This is based on the twin bees shuttle #C (46.0.0). Also see centinal (100.0.0). #C 54.0.1 #C 54.1.0 [DJB before 5/91] 2 p54 shuttles change the phase of a PD. #C Also see 29.3.0 and 36.1.0. #C ---------------------------------------------------------------------- #C 55.0.0 [DJB#162 1/26/86] #C ---------------------------------------------------------------------- #C 56.0.0 [DJB before 5/91] #C 56.0.1 "nonstandard p56 toadsucker" [RWG 10/25/94] See discussion #C at 60.0.0. #C 56.0.2 "nonstandard p56 toadflipper" [RWG 1994] See discussion at #C 60.0.0. #C ---------------------------------------------------------------------- #C 58.0.0 "p58, type 3 toadsucker" [RWG,MDN 10/25/94 (using larger #C p29s), DRH 12/13/94] See discussion at 60.0.0. #C ---------------------------------------------------------------------- #C 60.0.0 "p60 glider shuttle" [???? <=1971] #C 60.0.1 [AF 7/18/94] 2 p30 shuttles push a blinker up and down. #C #C A "toad hassler" is an oscillator in which a toad is changed by a #C pair of domino sparks above and below it. It either moves 1 unit #C sideways ("toadsucker") or changes its orientation ("toadflipper"). #C Amazingly, there are 5 different positions for the sparks which #C work; I call them "type -1" through "type 4", depending on the #C horizontal distance between the top and bottom sparks. The odd types #C are toadsuckers; the even ones are toadflippers. Given a period N #C oscillator which produces accessible domino sparks once per period, #C the resulting toad hasslers have period 4N if N is odd, 2N if N is #C even. However, there are also some toad hasslers in which the period #C is smaller, either because the sparks occur more than once per period #C (see 58.0.0) or because the interaction with the spark is more #C complicated (see 8.5.1-2, 16.2.1, and 56.0.1-2). Oscillators 60.1.0 #C to 60.1.4 show the 5 standard toad hassler geometries; see 8.3.3, #C 36.1.0-1, 108.0.0-1 for more examples. Toad hassling was apparently #C first discovered by RTW in 6/84, using sparks from PDs and snackers to #C give p60 and p36 oscillators. #C 60.1.0 "p60, type -1 toadsucker" #C 60.1.1 "p60, type 0 toadflipper" #C 60.1.2 "p60, type 1 toadsucker" #C 60.1.3 "p60, type 2 toadflipper" #C 60.1.4 "p60, type 3 toadsucker" #C #C 60.2.0 "p60 glider gun" or "twogun" #C [V. Everett Boyer & Doug Petrie <=1973] #C 60.2.1 "p60 end-to-end glider gun" #C 60.3.0 #C 60.3.1 "overwrought p60" [NDE 2/18/95] 2 modified Eurekas (30.2.0) #C and a p4 2-bit sparker (4.12.0) push a traffic light back #C and forth. #C 60.4.0 "metamorphosis II" [RTW 12/13/94] Illustrates a glider to #C LWSS reflection from a pair of p30 shuttles [found by #C Paul Rendell before 1/20/86, rediscovered by PC 12/9/94], and #C a symmetric collision between 2 LWSSs which makes 2 gliders. #C 60.4.1 This demonstrates a reaction [???? 1971?] in which gliders #C hitting a snake alternately create and destroy a boat. This #C can be used as a memory device (called a "boat-bit"); see #C 15240.0.0. #C 60.5.0 "twirling T-tetsons II" [RTW 1989] Period 60/4, symmetry #C type "nrk". #C 60.5.1 "p60 LWSS gun" [DRH 1/28/91?] A MW emulator deletes half of #C the outputs of a p30 LWSS gun. (There are also oscillators #C which can do the same for MWSS or HWSS streams; see 4.11.1 #C and 4.12.0.) #C 60.6.0 "p60 MWSS gun" This glider + pre-block -> MWSS reaction is #C very useful; see 46.3.1 and 60.6.0. #C 60.7.0 "pseudo p20 glider gun" [DRH 12/19/91] 3 p60 glider streams #C are merged to form a p20 stream. This uses a head-on #C collision between a glider and a pair of gliders to insert #C gliders into an existing glider stream. Using this reaction, #C a pseudo period N gun can be built for any N>=19. More #C complicated methods are known for getting periods 14 to 18. #C (Also see 46.5.0.) #C ---------------------------------------------------------------------- #C 72.0.0 [RTW 7/90] #C ---------------------------------------------------------------------- #C 75.0.0 "glider shuttle III" [RTW 9/84] #C ---------------------------------------------------------------------- #C 80.0.0 [DRH 10/28/94] A p16 (16.2.0) and a MW volcano (5.2.1) #C interact almost trivially. #C ---------------------------------------------------------------------- #C 88.0.0 [DRH 1994] A variant of 44.0.0. #C ---------------------------------------------------------------------- #C 90.0.0 "p90 glider shuttle" #C 90.0.1 [DIB 11/30/93] A glider shuttles between 2 pairs of p30 #C shuttles. At each end it turns into a boat and then back #C into a glider. The spark that turns the glider into a boat #C is symmetric, so this reaction can also be used to shift a #C glider's path by 2 units without reversing its direction. #C Also see 184.0.0 and 276.0.0. #C 90.1.0 "p90 glider gun" [DRH ????] #C ---------------------------------------------------------------------- #C 92.0.0 [RWG 5/28/92] 2 p46 shuttles push a beehive back and forth. #C Also see 46.0.1. #C 92.1.0 [NDE 11/23/94] 2 p46 shuttles push a blinker back and forth. #C 92.2.0 [DRH, NDE 1/15/95] 2 p46 shuttles repeatedly reverse a loaf. #C 92.3.0 [RTW 3/91] 2 p46 shuttles repeatedly convert blocks to #C gliders. Also see 30.1.2. #C 92.4.0 "p92 glider gun" [DRH 1/7/91] Made from 2 overlapping p46 #C guns. #C ---------------------------------------------------------------------- #C 96.0.0 "p96 Hans Leo hassler" [NDE 1/28/95] A p12 sparker #C (12.0.2) changes a traffic light into a B-heptomino; an #C eater and a figure 8 change it back. Also see 132.0.0, #C 144.1.0, and 156.0.0. #C ---------------------------------------------------------------------- #C 100.0.0 [RWG before 9/87] "centinal" Related to 46.0.0 and 54.0.0. RWG #C created a huge (13584x12112) p1100 glider gun from this. #C 100.0.1 "p100 traffic jam" [NDE 10/15/94] #C ---------------------------------------------------------------------- #C 105.0.0 A p15 PD (15.0.0) and a p7 (7.0.4) interact almost trivially. #C ---------------------------------------------------------------------- #C 108.0.0 "p108, type 0 toadflipper" See discussion at 60.0.0. #C 108.0.1 "p108, type 1 toadsucker" [DJB before 5/92] See discussion at #C 60.0.0. #C ---------------------------------------------------------------------- #C 110.0.0 "p110 traffic jam" [RWG 10/17/94] #C ---------------------------------------------------------------------- #C 120.0.0 "p120 glider gun" [DRH 1/13/91] A blocker can convert a #C period 8n+4 glider gun to period 16n+8. #C 120.0.1 [MDN ????] #C 120.1.0 "p120 LWSS gun" [DRH 1/28/91] A blocker can convert a #C period 8n+4 LWSS gun to period 16n+8. #C 120.2.0 "p120 MWSS gun" [????] This glider + pre-block -> MWSS #C reaction is very useful; see 46.3.1 and 60.6.0. #C 120.3.0 "p120 HWSS gun" [DJB ????] #C ---------------------------------------------------------------------- #C This mechanism was known for years before a way was found to make it #C work. A "lumps of muck" predecessor is hassled on the left starting #C around gen 15, causing its left half to disappear. The right half #C is hassled at the top starting around gen 55, causing another LoM #C predecessor to form in gen 62. The process is repeated, rotated 180 #C degrees. #C 124.0.0 [clock+eater+block by DRH ????, 4.11.1 by RWG 11/30/94] #C Smallest known version. #C 124.0.1 [DRH ????] An arbitrarily large agar can be built. #C 124.1.0 [eater3 by DJB? ????, MW emulator by MDN? ????, #C eater+p4 by DRH ????, 4.11.0 by ???? ????] #C 124.1.1 [4.12.0 by RWG 11/30/94, eater+p4 by DRH ????] #C ---------------------------------------------------------------------- #C 128.0.0 [DJB before 11/91] 2 B-heptominoes move around a track of length #C 256 gens formed from p8 oscillators. Also see 808.0.0. #C ---------------------------------------------------------------------- #C 132.0.0 "p132 Hans Leo hassler" [NDE 1995] A p12 sparker (12.0.2) #C changes a traffic light into a B-heptomino; a unix changes #C it back. Also see 96.0.0, 144.1.0, and 156.0.0. #C 132.0.1 [DJB before 8/94] A variant of 44.0.0. #C ---------------------------------------------------------------------- #C 135.0.0 [RWG 1989] A 2-glider shuttle, combining a rephaser and the #C reflections from 75.0.0. Also see 150.0.0. #C ---------------------------------------------------------------------- #C 138.0.0 [RWG ????] Glider loop based on a 'flawed' 180 degree #C glider reflection. The first reflection leaves behind a #C pond, which the next deletes, so gliders must occur in #C pairs. (But see 552.0.0.) The length of the loop may be #C anything of the form 138+184n. #C ---------------------------------------------------------------------- #C 144.0.0 [AF 7/21/94, DIB 8/8/94] Found by AF on a cylinder of #C height 22 (without the outer blocks) and originally #C stabilized using figure 8s. The use of blocks (which #C temporarily become loaves) was found by DIB. #C 144.0.1 "p144 glider gun" [RWG 7/22/94] Uses a spark from 72.0.0 #C to turn a block produced by 144.0.0 into a glider. #C 144.1.0 "p144 Hans Leo hassler" [NDE 1/4/95] A p12 sparker (12.0.2) #C changes a traffic light into a B-heptomino; an eater changes #C it back. Also see 96.0.0, 132.0.0, and 156.0.0. #C ---------------------------------------------------------------------- #C Also see p150 glider gun in 2700.0.0. #C #C 150.0.0 [DRH 1989] A 2-glider shuttle, combining a rephaser and the #C reflections from 90.0.0. Also see 135.0.0. #C 150.0.1 [RTW <=1989] A p150 2-glider shuttle, extensible to period #C 150+120N. Also see 165.0.0. #C ---------------------------------------------------------------------- #C 156.0.0 "p156 Hans Leo hassler" [NDE 1/4/95] A p12 sparker (12.0.2) #C changes a traffic light into a B-heptomino; an eater changes #C it back. Also see 96.0.0, 132.0.0, and 144.1.0. #C ---------------------------------------------------------------------- #C 165.0.0 [RTW <=1989] A p165 2-glider shuttle, extensible to period #C 165+120N. Also see 150.0.1. #C ---------------------------------------------------------------------- #C 184.0.0 [DRH 1/24/92] Glider shuttle based on 180 degree reflection: a #C p46 spark turns the glider into a block; the next spark turns #C it back into a glider. The period can be anything of the #C form 184+92n. Also see 276.0.0 and 90.0.1. #C ---------------------------------------------------------------------- #C 188.0.0 "pseudo p94 gun" [DJB,RCS,PC 7/11/94] A pre-honey farm #C interacts with an eater and a block, emitting a glider, #C creating a traffic light, and forming another pre-honey farm #C 47 gens later; this reaction is called "AK47". The new #C pre-h.f. interacts with another eater and block to recreate #C the original configuration. Unfortunately, the 2 traffic #C lights must be suppressed in order to make the process repeat #C every 94 gens. This reaction was found independently by DJB #C and RCS and was known for years before PC found a period 4 #C oscillator which could suppress the traffic lights. (A true #C p94 gun was built by DRH in 6/90, using 36 AK47s.) #C 188.0.1 "p188 glider gun" [DRH 7/19/94] #C ---------------------------------------------------------------------- #C 200.0.0 "p200 traffic jam" [RWG 10/16/94] (ERROR: This isn't an #C oscillator; it becomes one in gen 60.) #C ---------------------------------------------------------------------- #C 230.0.0 [DRH 3/19/92 (using early version of toaster)] 4-glider #C shuttle with period 230+40n. See comments for 42.0.0. #C 230.0.1 "obnoxious p230" [RWG 5/28/92] Sparks from a p46 shuttle #C interact 3 times with sparks from a p5 MW volcano; one #C interaction makes a temporary blinker; another makes a #C temporary glider. #C 230.1.0 [PC 6/28/94] p230 glider gun based on 2 LWSS reflections from #C p46 oscillators. In one, the LWSS is turned 90 degrees; in #C the other it becomes 2 parallel gliders. Also see 46.5.1. #C ---------------------------------------------------------------------- #C 240.0.0 2-glider shuttle. Uses the same 180 degree reflection as #C 60.0.0, combined with 2 rephasers. #C ---------------------------------------------------------------------- #C 246.0.0 [DRH 11/89 (p270+24n), 4/92 (p246)] 2-glider shuttle with #C period 246+24n. See comments for 42.0.0. #C ---------------------------------------------------------------------- #C 276.0.0 [DRH 1/24/92] Glider shuttle based on the same reflection #C as in 184.0.0. Also see 90.0.1 #C 276.1.0 "4-barrelled p276 glider gun" [DJB before 11/92] #C ---------------------------------------------------------------------- #C 282.0.0 [RWG 9/13/92] 2-glider shuttle. See comments for 42.0.0. #C ---------------------------------------------------------------------- #C 300.0.0 [MDN 10/27/94] Sparks from a pentadecathlon (15.0.0) and a #C centinal (100.0.0) interact to form a temporary block. #C ---------------------------------------------------------------------- #C 329.0.0 A p47 (47.0.0) and a p7 (7.0.4) interact almost trivially. #C ---------------------------------------------------------------------- #C 360.0.0 "p360 2-barelled glider gun" [DJB before 10/92] #C ---------------------------------------------------------------------- #C 400.0.0 "p400 glider loop" [RWG 1987] A glider bounces between 4 #C centinals. By expanding the loop and using more than one #C glider, oscillators of period 100N can be built for any N. #C ---------------------------------------------------------------------- #C 460.0.0 [DJB 1992, DRH 1995] p460 glider gun based on a reaction #C found by DJB which converts 2 gliders to 3 gliders. One #C glider escapes; the others are reflected by p46 shuttles #C to repeat the reaction. Given a period P oscillator which #C can reflect a glider 90 degrees, we can build a gun whose #C period is any multiple of P that's >= 452. (DJB originally #C used this to build a p500 gun, using centinals (100.0.0) to #C reflect the gliders.) #C ---------------------------------------------------------------------- #C 552.0.0 [RWG ????, DRH 1/23/92] Glider loop based on the same #C reflection as in 138.0.0. Here the ponds are deleted by a #C p8 blocker. The period of the loop can be anything of the #C form 138+184n, but the period of the oscillator is 4 times #C that. #C ---------------------------------------------------------------------- #C 690.0.0 [DRH 1/3/91] Sparks from a p46 shuttle interact 6 times with #C sparks from a p15 pentadecathlon; one interaction makes a #C temporary blinker. #C ---------------------------------------------------------------------- #C 808.0.0 "p808 glider gun" [DJB before 11/91] A B-heptomino moves around #C a track made of various eaters and p8 oscillators; it makes #C 4 moves each of durations 64, 65, and 73. Also see 128.0.0. #C (In 1996, DJB found several B-heptomino moves using only #C stable objects to form a track, thereby producing guns of #C all periods >= 62.) #C ---------------------------------------------------------------------- #C 856.0.0 "p856 glider gun" [DJB before 11/91] #C ---------------------------------------------------------------------- #C 2700.0.0 "crystallization and decay oscillator" [DRH 3/27/90] #C Extensible to period 2700+1950N. A p150 gun shoots gliders #C toward a pair of PDs. The first is reflected 180 degrees #C and hits the second, forming a honey farm. Subsequent #C gliders grow a crystal back toward the gun; every 11 #C gliders add another pair of beehives to the crystal. #C Eventually, an eater stops the growth and the crystal #C begins to decay: two successive gliders delete one pair of #C beehives. (This is based on an earlier pattern found and #C lost by RWG, using a p46 gun.) #C ---------------------------------------------------------------------- #C 15240.0.0 "p120-based PRNG" [DRH 3/21/92] Pseudo random number #C generator, based on an earlier pattern by RWG (a larger #C version of 40894.0.0). Produces a sequence of bits b[n], #C represented by gliders, satisfying the recurrence #C b[n] = b[n-1] XOR b[n-7]. The sequence has period 127, #C so the period of the pattern is 120*127. Increasing the #C separation between the NW and SE parts by 15N units #C diagonally changes the 7 above to K=7+N (N >= -4). The #C period of the sequence depends rather erratically on K: #C #C K | 2 3 4 5 6 7 8 9 10 11 12 13 14 15 #C P | 3 7 15 21 63 127 63 73 889 1533 3255 7905 11811 32767 #C #C K | 16 17 18 19 20 21 22 23 #C P | 255 273 253921 413385 761763 5461 4194303 2088705 #C #C K | 24 25 26 27 28 29 #C P | 2097151 10961685 298935 125829105 17895697 402653181 #C #C K | 30 31 32 33 #C P | 10845877 2097151 1023 1057 #C #C Also see 40894.0.0. (In 1996, DRH built a p30-based PRNG.) #C This uses a "boat-bit", a reaction in which gliders hitting #C a snake alternately create and destroy a boat. #C ---------------------------------------------------------------------- #C 40894.0.0 "p46-based PRNG" [RWG ????, DRH 1/10/95] Pseudo random #C LWSS generator. Produces a sequence of bits b[n], #C represented by LWSSs, satisfying the recurrence #C b[n] = b[n-1] EQV b[n-10]. The sequence has period 889, #C so the period of the pattern is 46*889. 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