at the top of my To-Do list, finally -- just have to get one item for Nathaniel's Game-of-Life textbook out of the way first.
As mentioned below, here's a draft of the comments that currently travel along with the DRH-oscillators pattern. I've updated several links and made miscellaneous other copy-editing changes.
Code: Select all
#N Stamp collection
#O Dean Hickerson, 2/2/2000; last updated 9/16/2000.
#C URLs corrected and list of missing periods updated 5/8/2009.
#C Updated by David Raucci, 3/30/2021.
#C
#C A collection of 934 oscillators of 120 different periods from 1
#C to 40894.
#C
#C The oscillators included here were found/built by many people over
#C many years. Dean Hickerson put the collection together in August 1995,
#C and worked on the header file off and on beween then and Sept. 2000.
#C
#C This file has since been updated in 2020 and 2021 by David Raucci,
#C converting it to a Python program that automatically updates
#C based on a text file input and includes more oscillators that were not
#C known in 1995.
#C
#C If you find any errors or can fill in any of the blanks, please contact
#C David Raucci on the conwaylife.com forums (username "hotdogPi"), or
#C open a GitHub repo issue at https://github.com/dvgrn/b3s23osc .
#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 https://www.conwaylife.com/ref/lifepage/patterns/bhept/bhept.html
#C for Buckingham's description of this, and
#C https://www.conwaylife.com/ref/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. In addition, the 2013 discovery
#C of the Snark allowed all oscillators of all periods 43 and higher.
#C There are 4 periods for which oscillators
#C are still unknown as of late 2020: 19, 34, 38, and 41.
#C (For period 34, we could use a noninteracting combination of p2 and p17
#C oscillators, but that's considered trivial.) All known nontrivial period
#C 39 oscillators are boring combinations of p3 and p13 oscillators.
#C
#C Building this collection would have been impossible without the help
#C of many people. In addition to those who found the oscillators, thanks
#C are due to 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
#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 AWH = Alan Hensel
#C DIB = David Bell DJB = David Buckingham
#C DRH = Dean Hickerson HH = Hartmut Holzwart
#C JHC = John Conway KS = Karel Suhajda
#C MDN = Mark Niemiec MM = Matthias Merzenich
#C NB = Nicolay Beluchenko NDE = Noam Elkies
#C PC = Paul Callahan RCS = Rich Schroeppel
#C RTW = Robert Wainwright 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 https://www.conwaylife.com/ref/lexicon/lex_home.htm
#C
#C The "rotor" consists of all cells in an oscillator that change state.
#C The "stator" consists of all cells that 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
#C To add an oscillator to oscillators.txt, all you need is the RLE and
#C optional comments. Make sure that there is no more than one #N or #O,
#C and #N comes before #O comes before #C. If the period is 1000 or more,
#C put a percent sign after the exclamation point at the end of the RLE.
#C While the file has oscillators sorted by period, the program will handle
#C them correctly even if they are out of order. If a pattern is not a
#C still life or oscillator, it will exclude it from the pattern, but it
#C will take an extra half second to figure this out unless it completely
#C dies first. Oscillators with width above 120 plus the digit width or
#C period >= 1000 with max bounding box expanding after generation 1000
#C are not supported unless the Python code is modified.
#C
#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 Frequencies listed are for 16x16 soups on an infinite grid. Most objects
#C are 10 percent more common on a large torus (AF 2004, 2048x2048), at the
#C expense of the block, which is about 6 percent less common, and the ship,
#C which goes from 1 in 20 to 1 in 90.
#N #N .0 Block [JHC group 1970]
#C Example of "*k" symmetry.
#C Used as an eater in many oscillators, too many to list. Also used as
#C a "rephaser" in P135, 150, 230, and 240 oscillators. In 47.0.0, it acts as
#C an induction coil, preventing a line of 6 from growing new cells.
#C Still life frequency: 1 in 2; the most common object in 16x16 soups;
#C on a large torus, the blinker is slightly more common.
#C 1.0.1 Tub [JHC group 1970]
#C Example of "*c" symmetry.
#C Used as an eater in most p29s, Eureka (P30), and 47.0.0.
#C A tub can stabilize an exposed line of five. This is usually done when reducing
#C population is the goal, but this collection is mainly optimized by bounding box,
#C where snakes are better.
#C Still life frequency: 1 in 65
#C 1.0.2 Boat [JHC group 1970]
#C Example of "/" symmetry.
#C A glider that hits a snake in the correct position will produce a boat while
#C leaving the snake intact. See P60 and P454.
#C Still life frequency: 1 in 14
#C 1.0.3 Ship [JHC group 1970]
#C Example of "xc" symmetry. Used as an
#C eater of traffic lights in P24, 36, 44, 48, and 92 oscillators.
#C Still life frequency: 1 in 20 in 16x16 soups, but this is because
#C they form from Herschels. On a large torus, they are 1 in 90.
#C 1.0.4 Beehive [JHC group 1970]
#C 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 A single beehive is also hassled in a P30 and P35 oscillator.
#C Still life frequency: 1 in 4
#C 1.0.5 Aircraft carrier
#C Example of ".e" symmetry.
#C One of the 35 hexominoes becomes an aircraft carrier after one generation.
#C .o..
#C oooo
#C ..o.
#C Despite this, it's still quite rare for a 6-cell pattern, although not as
#C rare as the snake or the clock.
#C It's more common in HighLife (B36/S23), as the pi heptomino generates two of them.
#C Still life frequency: 1 in 8,000
#C 1.0.6 Barge [JHC group 1970]
#C Example of "xk" symmetry.
#C Still life frequency: 1 in 1,000
#C 1.0.7 Snake [JHC group 1970]
#C Example of ".k" symmetry. Used in one P60 oscillator, 454.0.0,
#C and 15240.0.0 to convert a glider into a boat, which a
#C subsequent glider deletes.
#C Still life frequency: 1 in 30,000; rarest 6-bit still life
#C 1.0.8 Long snake
#C Also called a python, not to be confused with the programming language
#C Example of ".c" symmetry.
#C Rarest of the 7-bit still lifes in natural soups, at 1 in 700,000
#C 1.0.9 Long boat [JHC group 1970]
#C Still life frequency: 1 in 200
#C 1.0.10 Loaf [JHC group 1970]
#C Loaves can be flipped easily; this is part of how eater 3 works. See P8, 106,
#C and 133. Loaves can be flipped in other ways, too; see baker's dozen (P12),
#C loaflipflop (P15), one of the P20s, zweiback (P30), and popover (P32).
#C Still life frequency: 1 in 14
#C 1.0.11 Eater 1 [* 1971]
#C Also called a fishhook
#C This is a very useful still-life,
#C because of its ability to eat gliders (see period 30 section), beehives
#C (see period 30 section), and lightweight and middleweight spaceships
#C (see period 46 section), 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, eater 2, and eater 3, but
#C many others are sometimes useful, including the tub,
#C ship, and snake.
#C Still life frequency: 1 in 5,000
#C Rarest object that can be the result of a 2-glider collision.
#C 1.0.12 Long ship [JHC group 1970]
#C Still life frequency: 1 in 20,000
#C 1.0.13 Very long snake
#C Still life frequency: 1 in 2M
#C 1.0.14 Pond
#C Still life frequency: 1 in 70
#C Has a 4-cell predecessor
#C o..
#C .oo
#C .o.
#C 1.0.15 Hook with tail
#C Still life frequency: 1 in 3M
#C 1.0.16 Mango
#C Still life frequency: 1 in 2,750
#C 1.1.0 Long barge [JHC group 1970]
#C Still life frequency: 1 in 7,000
#C 1.1.1 Canoe
#C Also called sinking ship
#C Still life frequency: 1 in 200,000
#C 1.1.2 Shillelagh [Charles L. Corderman & Hugh Thompson 1971]
#C Still life frequency: 1 in 30,000
#C 1.1.3 Tub with tail [Charles L. Corderman & Hugh Thompson 1971]
#C Still life frequency: 1 in 125,000
#C 1.1.4 Hat
#C Found in 1971. Example of "-c" symmetry.
#C Still life frequency: 1 in 80,000
#C 1.1.5 Long hook with tail
#C Still life frequency: 1 in 17.5M
#C 1.1.6 Very long boat
#C Still life frequency: 1 in 100,000
#C Rarest still life with a 3-glider synthesis
#C 1.1.7 Long^3 snake
#C Rarest 9-bit still life, at 1 in 35M
#C 1.1.8 Integral sign
#C Still life frequency: 1 in 22,500
#C Anything with the same basic form as an eater can eat gliders, including the integral.
#C 1.1.9 Trans-boat with tail
#C Trans- and cis- have the same meanings as they do in organic chemistry.
#C Still life frequency: 1 in 60,000, which is 17 times as
#C common as cis-boat with tail
#C 1.1.10 Cis-boat with tail
#C Still life frequency: 1 in 1.1M
#C 1.1.11 Long canoe
#C Still life frequency: 1 in 4M
#C 1.1.12 Long shillelagh
#C Still life frequency: 1 in 2.5M
#C 1.1.13 Tub with long tail
#C Still life frequency: 1 in 3M
#C 1.1.14 Very long hook with tail
#C 1.2.0 Loop
#C Still life frequency: 1 in 700,000
#C 1.2.1 Very long ship
#C Still life frequency: 1 in 100,000
#C 1.2.2 Integral with hook
#C 1.2.3 Beehive with tail
#C Still life frequency: 1 in 500,000
#C 1.2.4 Cis-barge with tail
#C Still life frequency: 1 in 20M
#C 1.2.5 Claw with tail
#C Still life frequency: 1 in 4M
#C 1.2.6 Cis-hook with tail
#C 1.2.7 Block on table
#C Still life frequency: 1 in 350,000
#C 1.2.8 Barge siamese loaf
#C Still life frequency: 1 in 20M
#C 1.2.9 Very long barge
#C Still life frequency: 1 in 8M
#C 1.2.10 Long^4 snake
#C 1.2.11 Long integral
#C Still life frequency: 1 in 3M
#C 1.2.12 Boat with long tail
#C Still life frequency: 1 in 2.25M
#C 1.2.13 Cis-shillelagh
#C Unlike most objects called cis- or trans-, this still
#C life has two more cells than shillelagh
#C Still life frequency: 1 in 1.3M
#C 1.3.0 Integral with tub
#C Also called prodigal; the name came from "prod" = product
#C in relation to integrals providing sums
#C Still life frequency: 1 in 1.7M
#C 1.3.1 Trans-barge with tail
#C Still life frequency: 1 in 6M
#C 1.3.2 Fuse with two tails
#C 1.3.3 Boat-tie
#C Pun on bowtie
#C Still life frequency: 1 in 30,000
#C 1.3.4 Very long canoe
#C 1.3.5 Snake siamese snake
#C 1.3.6 Carrier siamese snake
#C Also called broken snake
#C Still life frequency: 1 in 2M
#C 1.3.7 Carrier siamese carrier
#C Still life frequency: 1 in 20M
#C 1.3.8 Tub with very long tail
#C 1.3.9 Very long shillelagh
#C Still life frequency: 1 in 18M
#C 1.3.10 Table and table
#C Still life frequency: 1 in 150,000
#C 1 in 10,000 in D2 symmetry (reflection)
#C 1.3.11 Cis-mirrored R-bees
#C Can be modified by either flipping one of the halves
#C and/or by moving one of them two cells up or down.
#C Still life frequency: 1 in 250,000
#C 1 in 4,000 in D2 symmetry (reflection)
#C 1.3.12 Bookends
#C Like the R-bees, one side can be mirrored and/or
#C shifted two cells.
#C Still life frequency: 1 in 900,000
#C 1 in 2,000 in D2 symmetry (reflection)
#C 1.3.13 Moose antlers
#C Still life frequency: 1 in 300,000
#C 1.4.0 Twin hat
#C Still life frequency: 1 in 600,000
#C 1.4.1 Dead spark coil
#C Usually formed by two pi heptominoes facing each other three cells apart.
#C Still life frequency: 1 in 175,000
#C 1 in 1,500 in D2 symmetry (reflection)
#C 1.4.2 Fourteener
#C Still life frequency: 1 in 700,000
#C 1.4.3 Beehive with two tails
#C Example of "-e" symmetry
#C 1.4.4
#C Example of "+c" symmetry
#C 1.4.5 Honeycomb
#C Much more common in rules with S8, as a line of six becomes a honeycomb
#C 1.4.6 Ship-tie
#C 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 Still life frequency: 1 in 400 on a 16x16 soup; 1 in 500 on a large
#C torus; one of the few objects to be rarer on a torus.
#C 1.4.7 Paperclip
#C Still life frequency: 1 in 14,000
#C 1.4.8 Big S
#C Still life frequency: 1 in 30,000 [MIT group 1971]
#C 1.4.9 Boat-ship tie
#C While rare (1 in 75,000), it's the most common still life with an odd
#C number of cells that's greater than 10.
#C 1.4.10 Block on dock
#C Still life frequency: 1 in 400,000
#C 1.4.11 Scorpion
#C 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 Still life frequency: 1 in 500,000
#C 1.4.12 Cap and table
#C Example of "-e" symmetry
#C 1.5.0 Half-bakery
#C As its name would suggest, they often appear in pairs.
#C Still life frequency: 1 in 1250
#C 1.5.1 Bi-pond
#C While not common (1 in 35,000), when it does appear, it's often in pairs.
#C A 9-cell predecessor produces a pair of them.
#C ..o..
#C ...o.
#C oo..o
#C ..ooo
#C ...o.
#C 1.5.2 Beehive on dock
#C Still life frequency: 1 in 300,000
#C 1.5.3 Spiral [RTW 1971]
#C Example of "rc" symmetry
#C 1.5.4 Eater 2 [DJB]
#C See periods 13, 225, and 226.
#C There are other forms of this eater, as long as it has the block in the corner;
#C see period 190 for this.
#C 1.5.5
#C Example of "+k" symmetry
#C 1.5.6
#C Example of "rk" symmetry
#C 1.5.7 7x9 eater
#C See P22, P25, and P94 sections.
#C 1.5.8 31.4 [Mike Playle, 2013]
#C Used in the Snark, which is probably the most important discovery in the 2010s.
#C 1.5.9 29-bit still life #1
#C The most common 29-bit still life in B3/S23/C1 on Catagolue.
#C Much more common than its size would suggest; 1 in 30B
#C 1.5.10 O quad loaf
#C Still life frequency: 1 in 27.5M; very common for 28 bits
#C 1.6.0 Eater 3 [DJB 6/22/77]
#C Eater 3 is technically a pseudo-still life, as the loaf is not required for
#C stability. It is, however, required for it to work as an eater.
#C See the period 8, 52, 55, 106, and 133 sections for the eater 3 in action, plus
#C P42, 50, 230, 246, and 282 for glider shuttles involving the eater 3.
#C 1.6.1 Eater 4 [DJB]
#C See the period 9, 11, 29, 30, and 58 sections for the eater 4 in action.
#C 1.6.2 [DJB]
#C Unnamed eater
#C ----------------------------------------------------------------------
#C 2.0.0 Blinker [JHC 3/70]
#C 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 99.0% of oscillators from a random soup are blinkers.
#C Most common object on a large torus; barely behind the block in
#C a 16x16 soup if you count only surviving objects.
#C Blinkers can be rephased; see 66P13, P35 traffic light hassler, and 47.0.0;
#C since these numbers are odd, they would not work without rephasing.
#C 2.0.1 Toad [SN 5/70]
#C Toads can be used as induction coils for rows that alternate 5 and 6 cells;
#C there are several examples in the P2 section.
#C See discussion of toad hasslers in the P60 section.
#C Oscillator frequency: 1 in 130, total frequency: 1 in 375,
#C although it might be a bit more common if
#C you count all created objects instead of just surviving ones.
#C 2.0.2 Beacon [JHC 3/70]
#C See the P24 shuttle and one of the P26 oscillators.
#C Oscillator frequency: 1 in 400, total frequency: 1 in 1200
#C 2.0.3 Clock [SN 5/70]
#C Example of ".kxk" symmetry.
#C Clocks are occasionally used in stabilizations;
#C see the P10, 14, 18, 20, and 124 sections.
#C Oscillator frequency: 1 in 750,000; very rare despite its size.
#C However, this still gives it rank #6.
#C 2.0.4 Bipole
#C Example of ".cxc" symmetry.
#C Oscillator frequency: 1 in 3M
#C 2.0.5 Tripole
#C Example of "/xk" symmetry.
#C Oscillator frequency: 1 in 100M
#C 2.0.6 Quadpole
#C Example of ".cxc" symmetry.
#C Oscillator frequency: 1 in 3.5M
#C More common than tripole, due to a reaction converting a ship into a quadpole.
#C 2.0.7 Fox [DHB 7/77]
#C Smallest asymmetric P2
#C 2.0.8 Phoenix 1 [MIT group 12/71]
#C Also known as flip-flops
#C Example of "rk*k" symmetry.
#C 2.0.9 Lei
#C There are six 12-bit P2 oscillators: lei, fox, phoenix, hexapole,
#C and two variants of beacon on table.
#C 2.0.10 By flops [RTW]
#C Example of "-c+e" symmetry.
#C There are only three 13-bit P2 oscillators: by flops, bipole tie boat,
#C and heptapole.
#C 2.0.11 Test tube baby
#C 2.1.0
#C There are 20 14-bit P2 oscillators. 7 include beacons, 7 include barber poles,
#C and the remaining 6 are eater plug, why not, test tube baby, and three unnamed.
#C 2.1.1 Why not [DJB 7/77]
#C 2.1.2 #C 2.1.3 Eater plug [RTW 2/73]
#C 2.1.4 Piston [* 1971]
#C Example of "-c+c" symmetry.
#C 2.1.5
#C Example of "-c+c" symmetry.
#C 2.1.6 Quad [Robert A. Kraus 4/71]
#C Example of "rk*k" symmetry.
#C 2.1.7
#C Example of "-c+e" symmetry.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 2.1.8 Blinkers bit pole [RTW 6/77]
#C Example of "n.e" symmetry.
#C 2.2.0 [DRH 5/20/93]
#C Example of "n.k" symmetry.
#C 2.2.1 [DRH 5/20/93]
#C Example of "n.k" symmetry.
#C 2.2.2 Cloverleaf [RTW before 6/72]
#C Example of "xc*c" symmetry.
#C 2.2.3 Block on griddle [RTW 7/72]
#C Can be stabilized other ways
#C Example of "n-e" symmetry.
#C 2.2.4 [DRH 5/20/93]
#C Example of "n-c" symmetry.
#C 2.2.5 [DRH 5/20/93]
#C Example of "n/" symmetry.
#C 2.2.6 Laputa [RCS 9/23/92]
#C Example of "n.e" symmetry.
#C 2.2.7 [DRH 5/20/93]
#C Example of "n.c" symmetry.
#C 2.2.8 Fore and back [AF 7/12/94]
#C Example of ".c+c" symmetry.
#C 2.2.9 Snake pit [MDN, 1972]
#C A period 2 oscillator with the same rotor as fore and back.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 2.3.0 Skewed quad
#C A period 2 oscillator and muttering moat.
#C 2.3.1 Spark coil [* 1971]
#C Usually formed by two pi heptominoes facing each other four cells apart.
#C Oscillator frequency: 1 in 15M
#C 2.3.2 Four boats
#C 2.3.3 [DRH 4/23/93]
#C Example of ".k+k" symmetry.
#C 2.3.4 [DRH 1994]
#C Infinitely extensible
#C 2.3.5 Light bulb [* 1971]
#C 2.3.6
#C Variant of light bulb
#C 2.3.7 Almosymmetric [* 1971]
#C Example of "n-e" symmetry.
#C 2.4.0 [DRH 4/23/93]
#C Example of ".c+c" symmetry.
#C 2.4.1 Example of ".cxc" symmetry.
#C 2.4.2 [DRH 4/23/93]
#C Example of "/xc" symmetry.
#C 2.4.3 [AWH 8/25/94]
#C Infinitely extensible
#C 2.4.4
#C Example of ".kxk" symmetry.
#C 2.4.5 [DRH 1973]
#C Example of "-e+e" symmetry. Infinitely extensible.
#C 2.5.0 [DRH 4/23/93, stator since improved]
#C Example of "-e+e" symmetry.
#C 2.5.1 [DRH 4/23/93]
#C Example of "-e+e" symmetry.
#C 2.5.2 [DRH 4/23/93]
#C Example of "-e+k" symmetry.
#C 2.5.3 [DRH 1994]
#C Infinitely extensible
#C 2.5.4 Scrubber [* 1971]
#C One of the most common results from a random soup on a 6x6 torus,
#C where the edges stabilize each other.
#C 2.5.5 [DRH 4/23/93]
#C Example of ".crc" symmetry.
#C 2.6.0 [AF 7/26/94]
#C Example of "rk*k" symmetry. A muttering moat.
#C 2.6.1
#C Example of ".e+e" symmetry.
#C 2.6.2
#C Example of "+k*k" symmetry.
#C 2.6.3 Barber pole [MIT group 1970]
#C Infinitely extensible
#C 2.6.4 [DRH 4/23/93]
#C Example of "rc*c" symmetry.
#C 2.6.5 [DRH 4/23/93]
#C Example of "xk*k" symmetry.
#C 2.7.0 [DRH 1994]
#C Infinitely extensible
#C 2.7.1
#C Example of "+k*k" symmetry.
#C 2.7.2 [RTW <1990]
#C Infinitely extensible
#C 2.7.3
#C Example of "xk*k" symmetry.
#C 2.8.0
#C Example of ".krk" symmetry.
#C 2.8.1 [RTW <1990]
#C Infinitely extensible
#C 2.8.2 [bottom end: RTW <1990; top end: DRH 1995]
#C Infinitely extensible
#C 2.8.3 [RTW <1990]
#C Infinitely extensible
#C 2.8.4 [Agar found by Robert A. Kraus 1971, stabilized by ????]
#C 2.9.0 [DRH 1994]
#C Infinitely extensible
#C 2.9.1 Ring of fire [DRH 9/24/92]
#C A "muttering moat"; i.e. an oscillator whose rotor consists of a closed loop of cells,
#C each of which touches exactly 2 others.
#C 2.9.2 Squaredance [Agar found by Don Woods, 1971, stabilized by DRH 3/25/93]
#C 2.10.0 [Agar found by Robert A. Kraus 1971, stabilized by DRH 12/13/94]
#C 2.10.1 #C 2.10.2 Houndstooth agar [DRH 3/30/94]
#C 2.11.0 Venetian blinds [DRH 9/12/92]
#C This uses diagonal edges for 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 horizontal edges don't exist.
#C 2.11.1 [DRH 12/4/94, improved by MDN 12/6/94]
#C ----------------------------------------------------------------------
#C 3.0.0 [DRH 8/89]
#C volatility 17/18
#C 3.0.1 [DRH 9/10/89]
#C 3.0.2 Bent keys [DRH 8/89]
#C 3.0.3 Short keys [DRH 8/89]
#C 3.0.4 [AF 7/13/94]
#C 3.0.5 Jam [AF 1988]
#C Used in another P3, a P18, and a P36 (don't confuse with mold).
#C Also don't confuse with traffic jams, which are completely unrelated.
#C 3.0.6 Trice tongs [RTW 2/82]
#C 3.1.0 [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.
#C 3.1.1 Candlefrobra [RTW 11/84]
#C Variant of Candelabra
#C 3.1.2 2 eaters [RWG 9/71]
#C 3.1.3 Cuphook [RCS 10/70]
#C 3.1.4 Stillater [RTW 9/85]
#C 3.2.0 Six Ls
#C A period 3 oscillator that has the same rotor as loading dock.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.2.1 #C 3.2.2 [NB, Dec 2012]
#C 3.2.3 [NB, Dec 2012]
#C 3.2.4 Caterer [DRH 8/4/89]
#C Provides a spark used in other oscillators
#C 3.2.5 Pulsar quadrant [DJB#46 7/73]
#C 3.2.6 1-2-3 [DJB#4 8/72]
#C 3.2.7 [AF 8/22/94, stator since reduced]
#C 3.2.8 Loading dock [DJB#3 9/72]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.3.0 Snake dance [RTW 5/72]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.3.1 New five [DRH 1/90]
#C 3.3.2 [DJB#92 7/26/76]
#C 3.3.3 Surprise [DJB#10 11/72]
#C 3.3.4 [DRH 11/27/94]
#C Volatility -> 1 as length increases. (Volatility = number
#C of rotor cells divided by total number of cells in rotor and stator.)
#C 3.4.0 Eaters plus [RTW 7/91]
#C Also called French kiss
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.4.1 Two pulsar quadrants [DJB#47 7/73]
#C 3.4.2 [RTW 4/82]
#C 3.4.3 Germ [DJB#9 9/72]
#C 3.4.4 Mini pressure cooker [RTW before 6/72]
#C 3.4.5 Cross [RTW 10/89]
#C One of the few known oscillators in which one phase is a polyomino.
#C 3.4.6 Runny nose [83bismuth38, 2017]
#C 3.4.7 [NB, Jan 2013]
#C 3.4.8 [NB, Jan 2013]
#C 3.5.0 Fire-spitting [NB, 09/2003]
#C 3.5.1 [DJB#7 <=1976]
#C Same rotor as in "2 eaters".
#C 3.5.2 [RTW 6/72]
#C 3.5.3 Triple caterer [DRH 8/89]
#C 3.5.4 [DRH 1/90]
#C Smallest known p3 (as of 1995) in which a corner of the
#C bounding box is active.
#C 3.5.5 [NB, Jan 2013]
#C 3.5.6 [NB, Jan 2013]
#C 3.5.7 [NB, Jan 2013]
#C 3.5.8 [NB, 2013?]
#C 3.6.0 Snake pit 2
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.6.1 Biting off more than they can chew [Peter Raynham 7/72]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.6.2 Pressure cooker [MIT group 9/71]
#C 3.6.3 Hustler [RTW 6/71]
#C 3.6.4 Double caterer [DRH 8/89]
#C 3.7.0 P3 rumbling river [DRH 11/26/94]
#C The rotor is connected and contained in a strip of height 2.
#C 3.7.1 #C 3.7.2 [NB, Jan 2013]
#C 3.7.3 Tubber [RTW before 6/72]
#C Rotor is confined to 2 parallel diagonals.
#C 3.7.4 Diamond ring [DJB#2 1972]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.7.5 [RTW 8/89]
#C 3.8.0 [AF 7/30/94 (symmetric form)]
#C 3.8.1 Star [HH 2/16/93]
#C Another polyomino.
#C 3.8.2 [HH 3/5/93]
#C Any of its four corners can be present or absent, and it will still work
#C 3.8.3 [DRH 9/18/89]
#C 3.8.4 [DRH 8/89]
#C 3.8.5 [DRH 8/89]
#C 3.9.0 2x3 cross [HH 2/26/93]
#C A larger version of Cross, which may be made any size.
#C 3.9.1 Pulsar [JHC 3/70]
#C The first known, and most commonly occurring, p3 oscillator.
#C Oscillator frequency: 1 in 5,000; ranked #4 behind blinker, toad, and beacon
#C About 25 percent rarer on a large torus than a 16x16 soup.
#C 3.9.2 [HH 3/5/93]
#C 3.9.3 Trans-skewed pulsar quadrants
#C 3.9.4 [DRH 1994]
#C 3.9.5 [DJB#103 6/3/77]
#C Rotor has symmetry type "-c", but stator can't be made symmetric.
#C 3.9.6 [DRH 10/89]
#C 3.10.0 Double ewe [RTW before 9/71]
#C 3.10.1 Skewed traffic light [RTW 8/89]
#C Uses two caterers and two jams, but could just as easily use four of either
#C 3.10.2 [DRH 11/27/94]
#C 3.11.0 #C 3.11.1 [DJB#79 6/6/76]
#C (DJB found the smallest form of this, with
#C just 1 2x3 rectangle. I don't know who found the wick.)
#C 3.11.2 [DRH 11/27/94]
#C 3.12.0 [RWG 9/22/94]
#C 3.12.1 Statorless P3 [Jason Summers, 2012]
#C This oscillator was the first discovered P3 to have volatility 1
#C 3.12.2 Quasar [RTW 8/71]
#C 3.13.0 [DIB 3/7/93]
#C 3.13.1
#C Period 3 agar
#C 3.14.0
#C Period 3 agar
#C ----------------------------------------------------------------------
#C 4.0.0 Mold [AF 1988]
#C Period 4/2, symmetry type "n/". Supplies a 1-bit spark
#C that's used, e.g., in several p28s and p32s and the p100 and p200 traffic light jams.
#C Most common natural p4 (1 in 20M), although still rare.
#C 4.0.1 Lightweight emulator
#C Has appeared semi-naturally (i.e. from symmetric soup) [RTW 6/80]
#C 4.0.2 Monogram [DRH 8/11/89]
#C Period 4/2, symmetry type "+c*c". Supplies a spark that's used in some P12s.
#C 4.0.3 [DJB#15 <1973]
#C Babbling brook
#C 4.0.4 [RTW 1989]
#C 4.0.5 Middleweight emulator [RTW 6/80]
#C Supplies a 1-bit spark
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.1.0 Heavyweight emulator [RTW 6/80]
#C Supplies a domino spark
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.1.1 [JS]
#C 4.1.2 Mazing [DJB#45 12/73]
#C Period 4/2, symmetry type "/xk".
#C Used in sixty-nine (P4) and popover (P32)
#C Oscillator frequency: 1 in 100M
#C 4.1.3 [DRH 8/89]
#C Period 4/2, symmetry type "/xk".
#C 4.1.4 20P4 [DRH before 4/92]
#C 4.1.5 [DRH 9/89]
#C 4.1.6 [DJB#104 6/3/77]
#C Babbling brook
#C 4.2.0 [DRH 8/89]
#C 4.2.1 [DJB#98 4/28/77]
#C Period 4/2, symmetry type "n-e".
#C 4.2.2 [DRH 10/89]
#C Related to the P60 toad hasslers.
#C 4.3.0 [DRH ????, DIB 12/11/94]
#C 4.3.1 #C 4.3.2 Achim's p4 [DJB#88 1976, AF 1988]
#C DJB found a larger form of this, using the same pieces that occur in siesta
#C (period 5) and sombreros (period 6). AF found the smaller version.
#C 4.3.3 [DRH 3/90]
#C Period 4/2, symmetry type "n/".
#C 4.3.4 [DRH 3/90]
#C Period 4/2, symmetry type "n/".
#C 4.3.5 [DRH 3/90]
#C Period 4/2, symmetry type "n/".
#C 4.4.0 Jack [RTW 4/84]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.4.1 Eater/block frob [DJB#51 <=1976]
#C 4.4.2 [DRH 11/10/94]
#C Babbling brook
#C 4.4.3 [DRH 8/89]
#C Period 4/2, symmetry type "n-e".
#C 4.4.4 [DRH 8/89]
#C Period 4/2, symmetry type "n-e".
#C 4.4.5 Penny lane [DJB#123 1972]
#C Like any row of 5, replacing the tub with a snake reduces the bounding
#C box by 1 row but increases the population by 2.
#C 4.4.6 [DJB#20 <1977]
#C 4.4.7 [DRH 12/10/94]
#C 4.5.0 [DRH 8/89, AF 1994]
#C 4.5.1 Confused eaters [DJB#49 before 1973]
#C Period 4/2, symmetry type "n/".
#C 4.5.2 [DJB#13 before 1973]
#C Babbling brook. Period 4/2, symmetry type "n/".
#C 4.5.3 [AF 7/17/94 (symmetric form), RWG,AWH 11/20/94]
#C 4.5.4 [RTW 11/90]
#C 4.5.5 #C 4.6.0 [12/6/94]
#C 4.6.1 [???? 1971]
#C 4.6.2 [RWG 9/17/94 (wick), 11/20/94 (ends)]
#C The repeating part of this wick may be attached to itself in 6 different ways.
#C 4.7.0 [MM, Oct 2013 (using WLS)]
#C (possibly known earlier)
#C 4.7.1 [DJB#23 <1973?]
#C 4.7.2 Pinwheel [SN 4/70]
#C Period 4/4, symmetry type "nrk".
#C 4.7.3 Clock II
#C Period 4/4, symmetry type "nrk".
#C 4.7.4 T-nosed P4 [RTW 1989]
#C Featured prominently in several P36 oscillators, as well as P8, 16, 44, 52, and 56.
#C 4.7.5 [DRH 8/89]
#C Period 4/2, symmetry type "n-C".
#C 4.7.6 [DJB#21 <1973]
#C 4.7.7 [DRH 12/10/94]
#C 4.8.0 [DRH 7/14/94]
#C 4.8.1 [DRH 4/6/92]
#C 4.8.2
#C Lightweight variant, also exists in middleweight and heavyweight variants
#C 4.8.3 Wavefront [DJB#24 <= 1976]
#C Rotor is confined to 2 parallel diagonals.
#C 4.8.4 Gray counter [???? 1971]
#C Goes through Gray codes 0-3; Gray codes and Gray counters are not exclusive
#C to Conway's Game of Life
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.8.5 [AF, AWH, DRH, 1994]
#C Only 3 cells are p4; the rest are p1 or p2.
#C 4.8.6 [AF 8/31/94 (symmetric form)]
#C 4.9.0 [DJB#69 <=1976]
#C 4.9.1 [DRH 12/10/94]
#C 4.9.2 Overweight emulator [RTW ????]
#C 4.9.3 [AWH 2/10/95]
#C 4.9.4 [DJB#28 before 1973?]
#C Rotor is p4/2, symmetry type "rk*k".
#C 4.9.5 Boss [DJB#30 1972]
#C 4.9.6 [DRH 12/10/94]
#C 4.10.0 [AF 8/23/94 (symmetric form)]
#C 4.10.1 [DRH 12/10/94]
#C 4.10.2 #C 4.10.3 Fountain [DRH 11/28/94]
#C Supplies a spark that's used in some P24 and P124 oscillators.
#C It can also be used (not shown) to double the period of a period 4N+2 MWSS stream.
#C 4.10.4 [RTW 9/89]
#C 4.11.0 [AF 7/13/94]
#C May be compressed horizontally by 1 or 2 cells.
#C 4.11.1 Octagon 4 [RTW 1/79]
#C An octagon of side 4. The edges can also be stabilized using eaters or toads.
#C This also works if a block is added in the center.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.11.2 [RTW 9/91]
#C 4.11.3 [DRH 1/10/95]
#C Period 4/4, symmetry type "nrc".
#C 4.12.0 #C 4.12.1 [DRH 1994]
#C A narrower but longer T-nosed p4
#C 4.12.2 Windmill [DRH 11/89]
#C 4.13.0 [RTW ????, AF 8/7/94]
#C An octagon of side 2, showing 2 ways to stabilize the edge.
#C 4.13.1 [MM, Jan 2011]
#C (based on a sparker by Noam Elkies)
#C 4.13.2 [RTW before 10/92]
#C The molds can be replaced by middleweight emulators.
#C 4.13.3 [DRH >=11/30/94]
#C Supplies a spark that's used in other oscillators.
#C It can also be used (not shown) to
#C double the period of a period 4N+2 HWSS stream.
#C 4.13.4 [DRH 1/10/95]
#C Period 4/4, symmetry type "nrc".
#C 4.14.0 [DRH 9/89]
#C An octagon of side 3, showing 4 ways to stabilize the edge.
#C 4.14.1 [DRH,RTW 9/89, AF 8/7/94]
#C An octagon of side 5, showing 4 ways to stabilize the edge.
#C 4.14.2 Sixty-nine [RTW 10/78]
#C Period 4/4, symmetry type "nrk".
#C 4.14.3 #C 4.15.0 [RTW 9/89 ]
#C Period 4/2, symmetry type ".crc".
#C 4.15.1 [DRH 1994]
#C 4.15.2 [DRH]
#C Period 4/2, symmetry type "+k*k".
#C 4.15.3 [AF,DRH 1994]
#C A larger octagon. The corners can also be
#C stabilized using eaters or toads.
#C 4.16.0 [DIB,DRH 12/12/94]
#C 4.16.1 [DRH 1994]
#C 4.16.2 [DRH 1994]
#C 4.16.3 [DRH 9/16/92]
#C Stabilized p4 agar, made of several parallel lines.
#C 4.17.0 [RTW 9/91, DRH 1/14/95]
#C First stabilization (not shown here) was found by RTW 9/91.
#C ----------------------------------------------------------------------
#C 5.0.0 Fumarole [DRH 9/3/89]
#C Supplies a domino spark that's used
#C in traffic jam oscillators such as those in period 25, 50, 100, 110, and 200.
#C (The domino spark in a HW volcano is more usable.)
#C 5.0.1 Silver's p5 [Stephen Silver, February 2000]
#C 5.0.2 Octagon 2 [Sol Goodman & Arthur C. Taber 1971]
#C Can be seen in one P25 and the P50 and P110 traffic jams.
#C Most common period 5 oscillator
#C 5.0.3 Scot's p5 [Scot Ellison, 06/08]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.0.4 Elkies' p5 [NDE 1997]
#C Has appeared naturally in an asymmetric soup
#C 5.0.5 5blink [Scot Ellison]
#C 5.0.6 Heart [RTW 1/82, DJB#145 8/15/84]
#C One of the few P5s to occur naturally, with many stator variants
#C 5.0.7 [DJB#163 2/19/87]
#C 5.1.0 [DRH]
#C There are 6 adjacent columns with only 1 active cell each.
#C 5.1.1 Swine [Scot Ellison]
#C extensible p5 oscillator; name short for Scot's p5 With INsErt.
#C 5.1.2 Montana [Scot Ellison, June 2011]
#C http://www.conwaylife.com/wiki/Montana
#C 5.1.3 Technician [DJB#33 1/73]
#C 5.1.4 Mathematician [DJB#34 1972]
#C 5.2.0 [DJB#160 1/6/87]
#C 5.2.1 [DJB#101 5/2/77]
#C 5.2.2 [DJB#44]
#C 5.2.3 Pedestle [DJB#39 1973]
#C Contains two copies of the rotor in technician
#C 5.2.4 Pseudo-barberpole [AF 8/22/94]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.2.5 [RTW 1/82 (DJB#146)]
#C 5.2.6 Pentant [DJB#85 7/11/76]
#C 5.3.0 101 [AF 8/19/94]
#C Named because one phase looks like it says "101", and 5 is 101 in binary
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.3.1 Siesta [DJB#57 1973]
#C 5.3.2 [DJB#84 7/76?]
#C 5.3.3 [AF 7/27/94]
#C 5.3.4 aVerage [DJB#35 1973]
#C 5.3.5 Middleweight volcano [DRH 4/6/92]
#C Supplies sparks that are used in some P25s and P230s.
#C 5.4.0 Chemist [DJB#38 1973]
#C 5.4.1 [DJB#87 7/15/76]
#C 5.4.2 Pentoad [RWG 6/77]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.4.3
#C Based on the pseudo-barberpole
#C 5.4.4
#C The basis of the P17 and P27 phase change oscillators.
#C 5.4.5 P5 pipsquirter [Dongook Lee, 2018]
#C A pipsquirter is an oscillator that emits a 1x2 spark vertically.
#C 5.4.6 [AF 7/13/94]
#C 5.5.0 [DJB#158 2/25/85]
#C 5.5.1 [DRH 1994]
#C 2 fumaroles hassle a long barge.
#C 5.5.2 [AF 8/7/94 (symmetric form), AWH 11/19/94]
#C 5.5.3 Toaster [DRH 4/1/92]
#C 5.5.4 [DJB#142 5/21/84]
#C 5.6.0 Electric fence [HH 10/20/92, DRH 11/23/92, 2/21/93]
#C A stream of 'ants' moves leftward from the 'source' at the
#C right to the 'sink' at the left.
#C 5.6.1 [Gabriel Nivasch 10/23/02]
#C 5.6.2 [11/19/94]
#C Also works even if the right part is not shifted two cells
#C 5.7.0 [DJB#151 9/29/84]
#C Optimized for bounding box, not for population
#C 5.7.1 [DRH 10/4/89]
#C 5.7.2 [DRH 1/26/95]
#C Another electric fence
#C 5.7.3 [DJB#114 6/2/77]
#C 5.8.0 Heavyweight volcano [Scot Ellison, 2007]
#C A period 5 oscillator that emits a rather isolated domino spark.
#C 5.8.1 Harbor [DJB#122 9/17/78]
#C (so-named because gen 3 consists of 4 ships and 8 boats)
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.8.2 Statorless p5 [Josh Ball]
#C Found in June 2016, using NB's version of WLS
#C Has volatility 1, meaning that no cell stays on for the entire period.
#C 5.8.3 [DJB#152 9/29/84]
#C 5.9.0 [DRH 12/2/94]
#C 5.9.1 [DJB#93 7/26/76]
#C 5.9.2 Three pentoads [RWG & Scott Kim]
#C ----------------------------------------------------------------------
#C 6.0.0 [NDE 7/3/97]
#C 6.0.1 Unix [DJB#48 2/10/76]
#C Produces a 1-bit spark that's used in many oscillators.
#C Only nontrivial p6 to occur naturally, excluding stator variants.
#C 6.0.2 [DRH/89]
#C Period 6/2, symmetry type "n/".
#C 6.0.3 Blonker [NB]
#C 6.0.4 A for all [DRH 3/6/93]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 6.0.5 P6 thumb [David Eppstein 6/26/2000]
#C 6.1.0 Sombreros [DJB#56 1972]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 6.1.1 [DJB#33 11/16/80]
#C 6.1.2 [DJB#58 <=1976]
#C 6.1.3 [DJB#59 <=1976]
#C 6.1.4 [DJB#102 6/3/77]
#C 6.1.5 Jason's p6 [AF 7/25/94]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 6.2.0 $rats [DJB#36 1972]
#C 6.2.1 Extremely impressive [DJB#78 8/76]
#C 6.2.2 [DJB#100 5/21/77]
#C 6.2.3 [AF 7/26/94]
#C 6.2.4 [DRH 9/22/94]
#C 6.2.5 [AF 8/7/94 (symmetric form)]
#C 6.2.6 [DJB#132 10/30/80]
#C 6.3.0 30P6.1
#C 6.3.1 [DJB#65 <=1976]
#C 6.3.2 [RTW 1989]
#C 6.3.3 P6 shuttle [Nicolay Beluchenko, 02/2004]
#C 6.3.4 Pipsquirter 1 [NDE 11/15/97]
#C 6.3.5 [AF 7/13/94]
#C 6.3.6 [RTW 1989]
#C 6.4.0 [DJB#117 9/1/77]
#C 6.4.1 [DJB#121 3/4/78]
#C 6.4.2 [DJB#110 6/19/77]
#C 6.4.3 64P6 [Dongook Lee and Matthias Merzenich]
#C 6.4.4 [DJB#99 5/12/77]
#C 6.4.5 [DJB#157 10/14/84]
#C 6.5.0 T-nosed p6 [AF 9/12/94]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 6.5.1 [DJB#141 4/25/84]
#C 6.5.2 Strictly volatile P6
#C Strictly volatile means that every cell oscillates at period 6
#C 6.5.3 [DRH 8/89]
#C Period 6/2, symmetry type ".e+e".
#C Volatility 1, but not strictly volatile.
#C 6.5.4 [DRH 8/89]
#C Period 6/2, symmetry type ".e+e".
#C Volatility 1, but not strictly volatile.
#C 6.6.0 [right end:RTW 10/78, middle and left end:DRH 10/89]
#C 6.7.0 [NDE 11/21/94]
#C 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 [DRH 9/89]
#C 6.8.1 [wick by DJB 1973, ends by DRH 1995?]
#C 6.9.0 Symmetric T-nosed p6 [AF 8/31/94]
#C 6.9.1 [RTW 11/16/94]
#C 4 unixes support a simple diagonal wick.
#C ----------------------------------------------------------------------
#C 7.0.0 28P7.1 [DRH, 11/1/98]
#C An unnamed period 7 oscillator that is tied as the smallest known.
#C 7.0.1 Burloaferimater [DJB#40 1972]
#C Only known oscillator with heat less than 2, with 10/7 or ~1.4
#C 7.0.2 37P7.1 [Scot Ellison]
#C A small period 7 sparker discovered in October, 2005
#C 7.0.3 [DJB#106 6/6/77]
#C Right half can also be turned upside-down and shifted up 2 units.
#C 7.0.4 [DRH 9/22/94]
#C 7.0.5 28P7.2 [DRH, 1998]
#C A period 7 oscillator that is tied with burloaferimeter and 28P7.1
#C as the smallest.
#C 7.1.0 38P7.2 [NB 2/17/09]
#C Can hassle two blocks, as seen in the P21 section. Also see P56.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 7.1.1 [MM, 18 Sep 2014 (using JLS)]
#C 7.1.2 [10/1/94]
#C 7.1.3 [DJB#77 <=1976]
#C 7.1.4 28P7.3 [Bullet51, 12/26/17]
#C 7.1.5 Airforce [DJB#41 1972]
#C Rotor consists of 2 copies of the rotor in burloaferimeter.
#C 7.1.6 41P7.2 [DRH, <=1998]
#C A period 7 oscillator with an isolated two-bit spark
#C 7.2.0 #DJB#113 9/7/81
#C 7.2.1 [DJB#109 6/19/77]
#C Supplies a domino spark.
#C 7.2.2 #DJB#113 6/21/77
#C 7.2.3 Hebdarole [NDE, November 1997]
#C ----------------------------------------------------------------------
#C 8.0.0 Smiley [AF 7/17/94]
#C Has appeared naturally
#C 8.0.1 Coe's p8 [Tim Coe, 08/97]
#C Has appeared naturally
#C 8.0.2 Achim's p8 [AF 7/20/94]
#C Period 8/2, symmetry type ".cxc".
#C Has appeared naturally
#C 8.0.3 Blocker [RTW]
#C Supplies a spark used in some P16, 24, 32, 40, 56, 72, 88,
#C 104, 120, 144, and 360 oscillators.
#C A blocker can filter a P60 glider stream into a P120 glider stream, as shown
#C in the P120 section.
#C Second most common p8 oscillator (1 in 130M), and third most common P5+ oscillator.
#C 8.0.4 Figure eight [SN 1970]
#C Supplies sparks used in many other oscillators, including other P8s.
#C Most common p8 oscillator (1 in 10M), but still very rare.
#C 8.0.5 R2D2 [Peter Raynham early 1970s (with a different stator), rediscovered and named by NDE 8/14/94]
#C 8.0.6 Tumbling T-tetson [RTW]
#C 8.1.0 nonstandard type 1 p8 toad sucker [DJB]
#C See discussion at period 60
#C 8.1.1 Cauldron [Don Woods, RTW 1971]
#C Also called crucible
#C 8.1.2 Hertz oscillator [JHC group 1970]
#C 8.1.3 [AF 8/26/94]
#C Supplies a 2-bit spark, which might be usable when the one in figure 8 fails.
#C 8.1.4 [DJB#90 7/16/76]
#C 8.1.5 [DJB#138 1/23/83]
#C 8.2.0 [DJB#94 7/29/76]
#C 8.2.1 nonstandard type 1 p8 toad flipper [DJB]
#C See discussion at period 60
#C 8.2.2 [NDE 7/18/97]
#C 8.2.3 Kok's galaxy [Jan Kok 1971]
#C Supplies a spark used in some P16, 24, 32, 40, 128, and 856 oscillators.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C Serves as Golly's logo
#C 8.2.4 [DRH 11/16/94]
#C A p8 variant of the p4 emulators
#C 8.2.5 Pyrotechnecium [DJB#42 1972]
#C 8.3.0 Roteightor [RTW 1972]
#C 8.3.1 [MM, Sep 2013 (using JLS)]
#C 8.3.2 [RTW 1989]
#C 8.3.3 Figure eights hassling long barge [RTW 9/84]
#C 8.3.4 [DJB#80 6/30/76]
#C Honey farm hassler
#C 8.3.5 [DJB#105 6/6/77]
#C 8.4.0 [Josh Ball, 12 Jun 2013]
#C 8.4.1 [DJB#115 6/22/77]
#C Loaf flipper
#C 8.4.2 [DJB#55 <=1976]
#C 8.4.3 Bottle [AF 8/7/94]
#C Also see "ship in a bottle", in the period 16 section
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 8.4.4
#C Toadflipper; see discussion in period 60 section
#C 8.4.5 [RTW 9/89]
#C Period 8/2, symmetry type "/xk".
#C 8.5.0 [KS 6/17/07]
#C 8.5.1 Figure eights hassling tub [AF 8/31/94]
#C 8.5.2 Multiple roteightors [DRH 1/90]
#C Can be infinitely extended
#C ----------------------------------------------------------------------
#C 9.0.0 29P9 [DRH 04/97]
#C The smallest known period 9 oscillator
#C 9.0.1
#C P9 domino sparker
#C 9.0.2 Worker bee [DJB#52 1972]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 9.0.3 Two worker bees
#C Can be infinitely extended. In fact, an infinite single row of
#C six on cells followed by two off cells will be a period 9 oscillator
#C without any stabilization needed.
#C 9.0.4 Snacker [MDN 1972]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 9.1.0 Two snackers
#C 9.1.1 [DJB#43 1972??]
#C 9.1.2 [DJB#83 7/10/76]
#C 9.1.3 P9 honey farm hassler [JP21 2/28/21]
#C 9.2.0 68P9 [carybe, 2018]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 9.2.1
#C 68P9 with worker bees
#C 9.2.2 48P9
#C A monomerized form of 68P9
#C 9.2.3
#C P9 domino sparker with high clearance. Found in 2020.
#C 9.3.0 [RWG 7/15/94]
#C Snackers hassling two blocks
#C 9.3.1 [RWG 7/15/94]
#C Snackers hassling two blocks
#C 9.3.2 [DJB#155 10/9/84]
#C Stator is Eater 4. See P11 section for another example.
#C ----------------------------------------------------------------------
#C 10.0.0 37P10.1
#C 10.0.1 24P10 [MM, Nov 12, 2010]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 10.0.2 55P10 [Bullet51, 2018]
#C Hassles a traffic light in one P20.
#C Also exists in a skewed variant; see the P50 section.
#C 10.0.3 [DRH, 2008 (using dr)]
#C 10.0.4 42P10.3 [DJB#76 <=1976]
#C 10.1.0 [DJB#161 1/21/86]
#C 10.1.1 [DRH, 2008 (using dr)]
#C 10.1.2 [DJB#153 9/30/84]
#C 10.1.3 [MM 4/10/10]
#C 10.1.4 [DRH, 2008 (using dr)]
#C 10.1.5 [DRH, 2008 (using dr)]
#C 10.2.0 P10 traffic light hassler [DJB#139 5/1/83]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 10.2.1 [DRH, 2008 (using dr)]
#C 10.2.2 [MM (using Nicolay's version of randagar)]
#C 10.2.3 [NB 3/16/09]
#C 10.3.0 [DRH 2/16/95]
#C 2 p5s hassle a blinker. DRH's 1995 file included a similar oscillator where
#C 4 p5s hassled a blinker, but it was huge and removed from this file to save space.
#C 10.3.1 128P10.2 [NB, 2009]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C ----------------------------------------------------------------------
#C 11.0.0 [MM, Aug 2014]
#C 11.0.1 38P11.1 [DJB#112 6/20/77]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 11.0.2 [DRH, 2008]
#C 11.0.3 [MM, Aug 2014]
#C 11.0.4 Rattlesnake [DRH, 2016]
#C 11.1.0 [DRH, 2008]
#C 11.1.1 [MM, Oct 2014]
#C 11.1.2 [DRH, 2008]
#C 11.1.3 [MM, Aug 2014]
#C 11.1.4 [MM, Sep 2014]
#C 11.2.0 [MM]
#C 11.2.1 Achim's p11 [AF 8/4/94]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 11.2.2 [DJB#156 10/9/84]
#C Stator is Eater 4. See P9 section for another example.
#C 11.2.3 P11 pinwheel [NB, May 2009]
#C Rotationally symmetric
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 11.3.0 Jason's p11 [JS April 2003]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C ----------------------------------------------------------------------
#C 12.0.0 Carnival shuttle
#C Supported by monograms; middleweight emulators work too
#C 12.0.1 #C 12.0.2 [RTW 9/84]
#C 12.1.0
#C Billiard table
#C 12.1.1 #C 12.1.2 Dinner table [RTW 1972]
#C Period 12/4, symmetry type "nrc".
#C 12.1.3 [NDE 7/18/97]
#C 12.1.4
#C Billiard table
#C 12.2.0 [DJB <1980, RTW 1989]
#C 12.2.1 35P12 [MM, 2015]
#C 12.2.2 [NDE 10/15/98]
#C 12.3.0 Crown [NDE 1/93/95]
#C Supplies a spark used in other oscillators; see 132 and 156 for examples
#C 12.3.1 #C 12.3.2 Eye of Sauron [NB 3/26/09]
#C Also known by its systematic name 44P12.3
#C An option to stabilize 168.0.0, although not shown since it
#C has a larger bounding box than what's shown there.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 12.3.3 [NDE 5/23/96]
#C 12.4.0 [JS January 2004]
#C 12.4.1 [DJB#159 1986?]
#C 12.4.2 2c/3 signal
#C There is no known way to turn a 2c/3 signal, but if there is,
#C there would be a way to create any period above a certain number;
#C giving an example for 34, 38, and 41, and if small enough, 19.
#C 12.4.3 [DJB#131 10/26/80]
#C 4 baker's dozens, using only stable objects and each other for support.
#C 12.5.0
#C P12 honey farm hassler
#C 12.5.1 #C 12.5.2 Baker's dozen [RTW 8/89]
#C 12.5.3 Period 12 toadflipper
#C 12.5.4 Period 12 toadsucker
#C 12.6.0 [DRH 1/4/95]
#C A larger version of crown, with a more accessible spark.
#C 12.6.1 Two Eyes of Sauron hassling unnamed object
#C 12.6.2
#C Four P6 sparkers hassling block
#C 12.7.0 Dinner table extension
#C 12.7.1 [MDN, DRH >~2/20/95]
#C A wick based on Crown, using a p3 multiple caterer.
#C 12.8.0 [NDE 6/9/95]
#C R-pentomino hassler
#C ----------------------------------------------------------------------
#C 13.0.0 [Scorbie, Oct 2014]
#C 13.0.1 53P13 [Bullet51, 2015]
#C 13.0.2 [MM, Sep 2014]
#C 13.0.3 Buckingham's p13 [DJB#96 7/31/76]
#C 13.0.4 [MM, 9/15/14]
#C 13.1.0 [DRH, 2008]
#C 13.1.1 [MM, Sep 2014]
#C 13.1.2 66P13 [Bullet51, 2019]
#C 13.1.3 Beluchenko's p13 [NB, 2009]
#C The smallest known period 13 oscillator.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 13.1.4 [MM, Aug 2014]
#C 13.2.0 [MM, Aug 2014]
#C 13.2.1 [MM, Oct 2014]
#C 13.2.2 [MM, Sep 2014]
#C ----------------------------------------------------------------------
#C 14.0.0 Tumbler [George Collins, Jr. 1970]
#C Period 14/2, symmetry type "-c+c".
#C Only known p14 oscillator until 1997
#C Fourth most common oscillator with period above 8, after pentadecathlon
#C and two versions of queen bee.
#C 14.0.1 44P14 [DRH, 21 Apr 1997]
#C Billiard table
#C 14.0.2 [MM, 19 Sep 2014 (using JLS)]
#C Based on a phase shift reaction by Noam Elkies
#C 14.0.3 34P14 shuttle [carybe, 2018]
#C Was found via symmetric soup search
#C 14.1.0 Tetradecathlon
#C Sparks from the 34P14 shuttles make the pentadecathlon skip a generation.
#C 14.1.1 [MM, Sep 2014 (using dr)]
#C 14.1.2 [MM, 18 Sep 2014 (using JLS)]
#C based on reactions by Dean Hickerson
#C 14.1.3 [MM, Aug 2014 (using dr)]
#C 14.2.0 [JS 1/7/06]
#C ----------------------------------------------------------------------
#C 15.0.0 Pentadecathlon [JHC 1970]
#C Frequently used in higher-period oscillators. See every multiple of
#C 15 up to 165 (except 105, where there aren't any in this collection).
#C They can also have their phase changed; see P9, 14, 36, 54, and 58.
#C Oscillator frequency: 1 in 400,000; ranked #5
#C About 25 percent rarer on a large torus than in a 16x16 soup
#C 15.0.1 Karel's p15 [KS 12/11/02]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 15.0.2 [MM, Sep 2014 (using dr)]
#C 15.0.3 [MM, Aug 2014 (using dr)]
#C 15.0.4
#C P15 traffic light hassler
#C 15.1.0 [RTW 10/78]
#C 2 PDs hassle 2 blocks symmetrically.
#C 15.1.1 Jolson [RTW 11/84]
#C 2 PDs hassle 2 blocks asymmetrically.
#C 15.1.2 Two pentadecathlons hassling barge [DJB 7/73]
#C 15.1.3
#C P15 traffic light hassler
#C 15.2.0 [DJB 3/73]
#C Four pentadecathlons hassling four blocks
#C 15.2.1 p15 biblock hassler [DRH 2/21/95]
#C 15.2.2 112P15 [thunk, 4/4/16]
#C Discovered via symmetric soup
#C 15.2.3 [KS 6/13/07]
#C 15.3.0 Loaflipflop [RTW 1990]
#C 4 pentadecathlons hassle a loaf.
#C ----------------------------------------------------------------------
#C 16.0.0 #C 16.0.1 p16 biblock hassler [NDE 2/20/95]
#C 2 1-bit sparks (from a blocker and a mold) hassle a pair of
#C blocks. Sparks can also come from oscillators of period 5 (see P15),
#C 6 (see P18), 7 (see P21), 12 (see P24), 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 period 52) or use the
#C spark for the two pond and two block reaction (see periods 32 and 36).
#C 16.0.2 Rob's p16 [Rob Liston, 2020]
#C Found via asymmetric soup search
#C 16.0.3 Rich's p16 [Rich Holmes, 7/5/16]
#C Found via symmetric soup search
#C 16.0.4 #C 16.1.0 Achim's p16 [AF 7/27/94]
#C Period 16/2, symmetry type "rc*c".
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 16.1.1 Symmetric p16 biblock hassler [NDE 2/21/95]
#C 16.1.2 2 pre L hassler [RTW 7/83]
#C 4 blockers hassle a pair of pre-loafs. Period 16/2, symmetry type ".k+k".
#C 16.1.3 Ship in a bottle [RWG 8/7/94]
#C Period 16/2, symmetry type "/xk".
#C 16.1.4 68P16 [carybe, 2018]
#C Discovered via symmetric soup
#C 16.2.0
#C P16 honey farm hassler
#C 16.2.1 Sailboat [RTW 6/84]
#C 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 16.2.2
#C P16 honey farm hassler
#C 16.3.0
#C An extension of Achim's p16
#C 16.3.1 Achim's other p16 [AF 8/7/94 (on a 32x32 torus), RWG 8/17/94]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C ----------------------------------------------------------------------
#C 17.0.0 54P17.1 [DRH]
#C The first period 17 oscillator to be found. Discovered on April 27,
#C 1997.
#C 17.0.1 Honey thieves [MM]
#C The smallest known period 17 oscillator in terms of population
#C as of December 2020.
#C 17.0.2
#C The center oscillates with period 5, but every 3 times, it is extended
#C two generations, making it period 17. Similarly, the outer portions would
#C oscillate with period 8 if they didn't interact with the center.
#C Also see the period 27 section.
#C ----------------------------------------------------------------------
#C 18.0.0 p18 biblock hassler [NDE 2/20/95]
#C 18.0.1 Merzenich's p18 [MM, June 2011]
#C The first period 18 billiard-table oscillator
#C 18.0.2 P18 honey farm hassler
#C 18.1.0
#C P18 lumps of muck hassler
#C 18.1.1 P18 traffic light hassler [NDE 5/20/96]
#C 18.1.2
#C A 10n-2 phase shift oscillator.
#C 18.1.3
#C An 8n+2 phase shift oscillator.
#C 18.2.0 [JS February 2004]
#C 18.2.1 [JS 4/10/01]
#C 18.2.2 Four eaters hassling four bookends [Jason Summers, 10/16/2002]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 18.3.0 [DJB before 5/91]
#C Period 18/2, symmetry type "n.e".
#C 18.3.1 P18 beehive hassler
#C 18.3.2 [JS 2/26/02]
#C 18.4.0 [Gabriel Nivasch 9/1/95]
#C 18.4.1 [Sokwe 12/29/20]
#C 18.4.2
#C Period 18 R-pentomino hassler. Found in 2020.
#C 18.5.0 [DRH 1/1/195]
#C 2-glider shuttle. See comments for P42 glider shuttle.
#C ----------------------------------------------------------------------
#C 20.0.0 [JS 12/02]
#C 20.0.1 #C 20.0.2 [NDE 3/22/95]
#C A period 9+11 traffic light hassler.
#C 20.1.0 [NDE 4/2/95]
#C A period 10+10 traffic light hassler.
#C 20.1.1 #C 20.1.2 [NDE 6/29/95]
#C Sparks from some p4 and p5 oscillators hassle a loaf.
#C 20.1.3 #C 20.2.0 P20 pre-pulsar hassler
#C ----------------------------------------------------------------------
#C 21.0.0 P21 honey farm hassler
#C 21.0.1
#C A 10n+1 phase shift oscillator.
#C 21.0.2 [NDE 9/7/99]
#C Two ponds and two blocks in a particular configuration, when a pair of one-bit
#C sparks is applied to them, becomes the original configuration again.
#C This reaction is very versatile and is used in many oscillators. The minimum
#C repeat time is 20. Other oscillator periods using this reaction are
#C 24, 26, 27, 30, 32, and 36.
#C 21.1.0 #C 21.1.1
#C Compare to P18 biblock hassler
#C 21.1.2 [RTW 2/21/95]
#C A period 10+11 traffic light hassler.
#C ----------------------------------------------------------------------
#C 22.0.0 Champagne glass [DRH 4/19/97]
#C 22.0.1 Jason's P22 [Jason Summers, 2000]
#C Can be used to make a P22 glider gun, the second smallest true period known after 20.
#C 22.0.2 [Jason Summers 9/8/05]
#C 22.0.3 48P22.1 [NB, 2009]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 22.1.0 P22 honey farm hassler
#C 22.1.1 168P22.1 [NDE, 1997]
#C First P22 to be found
#C 22.1.2 P22 pre-pulsar hassler
#C 22.1.3 True period 22 gun [David Eppstein]
#C The first true period 22 gun constructed. Found in August 2000.
#C Contains two copies of 36P22
#C 22.2.0 P22 lumps of muck hassler [Aidan F. Pierce, 2015.]
#C Contains two copies of Jason's P22.
#C ----------------------------------------------------------------------
#C 23.0.0 David Hilbert [Luka Okanishi, 2019]
#C The only known period 23 oscillator except for trivial variations.
#C 23 is the most recent previously-undiscovered oscillator period to be discovered.
#C ----------------------------------------------------------------------
#C 24.0.0 #C 24.0.1 p24 lumps of muck hassler [Sokwe 12/27/20]
#C Uses two copies of Scorbie's p6 sparker
#C 24.0.2 #C 24.1.0 Dueling banjos [Apple Bottom, 2019]
#C Was found via symmetric soup search
#C 24.1.1 p24 shuttle [KS, 10/17/02]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 24.1.2 Period 24 biblock hassler
#C See period 16 biblock hassler for explanation
#C Uses an Eye of Sauron (P12) and mold (P4)
#C 24.2.0 [NDE 11/20/94]
#C 24.2.1
#C See P21 section for discussion.
#C 24.2.2 p24, type 2 toadflipper. [RWG 1994]
#C See discussion in P60 section
#C 24.3.0 [RWG 11/29/94]
#C 24.3.1 [RWG 11/29/94]
#C 24.3.2 [JS 5/8/07]
#C 24.3.3 [JS 6/19/05]
#C 24.4.0
#C Period-24 glider gun
#C The gun actually named "Period-24 glider gun" is a different gun,
#C with too large a bounding box to show here.
#C Based on dueling banjos
#C 24.4.1 P24 honey farm hassler
#C 24.4.2 Four p24 shuttles hassling Octagon 2
#C Octagon 2 is period 5, but it skips a generation every time the p64s
#C give it sparks.
#C ----------------------------------------------------------------------
#C 25.0.0 [NDE 11/5/94]
#C 25.0.1 [NDE 9/23/94 (with toasters instead of eaters), DRH 10/19/94]
#C Based on pushing 2 or more traffic light
#C predecessors 3 units in 14 gens and pushing them back in 11 gens.
#C 25.1.0 88P25 [MM 1/10/2016]
#C p25 honey farm hassler
#C 25.1.1 P25 pre-pulsar shuttle
#C 25.1.2
#C p25 honey farm hassler
#C 25.2.0 [MDN 1/9/96; heavyweight volcano since improved]
#C 25.2.1 [JS 5/14/07]
#C 25.2.2 [DJB 10/96 (left half), NDE 12/13/97 (right half)]
#C 25.3.0
#C ----------------------------------------------------------------------
#C 26.0.0 P26 biblock hassler
#C See P16 for discussion of biblock hasslers.
#C 26.0.1
#C See P21 section for discussion.
#C 26.0.2 P26 queen bee shuttle [JP21 2/8/21]
#C Optimized for bounding box. There are other variants with lower
#C population but a larger bounding box.
#C 26.1.0 [DJB#140 1/18/83]
#C 26.1.1
#C P26 honey farm glider shuttle
#C Unlike most glider shuttles, this one requires a glider to remain stable;
#C the reaction fails without a glider every cycle.
#C ----------------------------------------------------------------------
#C 27.0.0
#C The bottom right corner has the P7 burloaferimeter rotor, but every four
#C times, it skips a generation, making it P27.
#C 27.0.1
#C p27 traffic light hassler
#C 27.0.2 94P27.1 [JS 2005]
#C The smallest known period 27 oscillator as of April 2009.
#C See P21 section for discussion.
#C 27.1.0
#C The center oscillates with period 5, but every 5 times, it is extended
#C two generations, making it period 27.
#C Also see the period 17 section.
#C 27.1.1 56P27 [NB, May 2010]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C ----------------------------------------------------------------------
#C 28.0.0 [thunk, 2016]
#C 28.0.1
#C Most 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.
#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 28.0.2 [RWG 7/31/94]
#C 28.0.3
#C This is a 9n+1 phase shift oscillator.
#C 28.1.0 P28 R-pentomino shuttle
#C Uses two tetradecathlons supported by four P34.14s
#C 28.1.1 P28 type 2 toadflipper
#C Uses two tetradecathlons supported by four P34.14s
#C See P60 section for toadsucker/flipper explanation
#C 28.2.0 P28 type 1 toadsucker
#C Uses two tetradecathlons supported by four P34.14s
#C See P60 section for toadsucker/flipper explanation
#C 28.2.1 Karel's p28 [KS 6/12/07]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 28.3.0 P28 glider shuttle
#C Uses four 34P14 shuttles
#C ----------------------------------------------------------------------
#C 29.0.0 #C 29.0.1 p29 traffic farm hassler [Ian Fomichev 1/2/15]
#C The first p29 discovered not to be based on the pre-pulsar
#C 29.1.0 p29 pentadecathlon hassler [RWG ????, DRH 12/13/94]
#C 2 copies of 29.0.1 change the phase of a PD. Supplies a 2-bit spark
#C that's used in 58.0.1.
#C 29.1.1
#C ----------------------------------------------------------------------
#C 30.0.0 Queen bee shuttle [RWG 1970]
#C The central 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.
#C Also see periods 60, 90, 120, 180, 210, and 300. There's also a P26 queen bee
#C shuttle that skips a few generations.
#C The second most common oscillator with period greater than 8,
#C after pentadecathlon. Has cis and trans versions.
#C 30.0.1
#C 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 30.0.2 [RTW]
#C 2 p30 shuttles repeatedly convert blocks to gliders.
#C 30.1.0 [DIB 9/1/92]
#C 2 p30 shuttles repeatedly reverse a loaf.
#C 30.1.1
#C Two pentadecathlons hassling traffic lights
#C 30.1.2 Gosper glider gun
#C 30.2.0 [NDE 10/30/94]
#C 2 p30 shuttles repeatedly change the phase of a blinker.
#C 30.2.1 Eureka [DJB#130 8/16/80]
#C The simplest pulsar hassler.
#C Can also be skewed, by moving one half up 2 units.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 30.2.2
#C Honey farm hassler
#C 30.2.3 Zweiback [MDN 2/13/95, since improved]
#C 30.3.0 Four pentadecathlons hassling four ships
#C 30.3.1
#C Two Karel's p15s hassling two ponds and two blocks
#C See P21 section for discussion.
#C 30.3.2 [DRH 2/14/95, since improved]
#C 4 p5s hassle a beehive.
#C 30.4.0 Pulshuttle V [RTW 5/85]
#C 30.4.1 P30 LWSS gun
#C 30.5.0
#C Honey farm hassler
#C 30.5.1 Hectic [RTW 9/84]
#C Period 30/2, symmetry type ".crc".
#C 30.5.2
#C 6 gliders in a 180 gen loop. This use of a queen bee
#C as a reflector is called a "buckaroo".
#C ----------------------------------------------------------------------
#C 31.0.0 Merzenich's p31 [MM 11/5/10]
#C The first known period-31 oscillator
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 31.0.1
#C P31 honey farm glider shuttle
#C Note that this oscillator only has 180 degree rotational symmetry, not 90 degree.
#C Unlike most glider shuttles, this one requires a glider to remain stable;
#C the reaction fails without a glider every cycle.
#C ----------------------------------------------------------------------
#C 32.0.0 Gourmet [DJB March 4, 1978]
#C Period 32/4, symmetry type "nrk".
#C 32.0.1 [yujh 12/27/20]
#C 32.0.2 [RTW 5/85]
#C 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 32.1.0 68P32.1 [MM, 12/31/09]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 32.1.1 Pi portraiter [RTW 1984 or 1985]
#C Period 32/4, symmetry type "nrk".
#C 32.1.2 P32 blinker hassler [NDE, 2010]
#C Hassled by a blocker and a blocked p4-3.
#C 32.1.3 [NDE 1/26/95]
#C Traffic light hassler
#C Period 32/2, symmetry type "-c+e".
#C 32.2.0 #C 32.2.1 Popover [RTW August 1984]
#C Period 32/4, symmetry type "nrk".
#C 32.2.2
#C See P21 section for discussion.
#C ----------------------------------------------------------------------
#C 33.0.0 Jason's P33 [Jason Summers, 2000]
#C Can be used to make a P33 glider gun
#C ----------------------------------------------------------------------
#C 35.0.0 P35 honey farm hassler [Dongook Lee]
#C Found on 9 January 2016, with a hacked version of ptbsearch
#C 35.0.1 50P35 [Jason Summers, 2002]
#C 35.0.2 P35 traffic light hassler
#C 35.0.3 P35 beehive hassler [DRH, 2/14/1995, since improved]
#C The first known period 35 oscillator
#C ----------------------------------------------------------------------
#C 36.0.0 22P36 [NDE 1/29/95]
#C P36 traffic light hassler
#C The smallest known oscillator over period 30 by population, with 22 cells
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 36.0.1 [JS 7/23/04 (without phase changing oscillator)]
#C P36 B-heptomino hassler; phase-changing oscillator is optional
#C 36.0.2 P36 traffic jam [RWG 10/14/95]
#C 36.1.0 [NDE 11/20/94]
#C 36.1.1 p36, type 0 toadflipper
#C See discussion in period 60 section
#C 36.1.2 p36, type 1 toadsucker
#C See discussion in period 60 section
#C 36.2.0
#C P36 honey farm hassler
#C 36.2.1 #C 36.2.2
#C Two P18 biblock hasslers hassle two ponds and two blocks.
#C See P16 section for biblock hasslers and P21 section for two pond and
#C two block hasslers.
#C 36.3.0 P36 shuttle [carybe, 2018]
#C Found via symmetric soup search
#C 36.3.1
#C P36 honey farm hassler
#C 36.4.0 P36 lumps of muck hassler [JS January 2004]
#C 36.4.1 #C 36.5.0 [NDE 11/23/94]
#C ----------------------------------------------------------------------
#C 37.0.0 Beluchenko's P37 [NB, April 2009]
#C The first period 37 oscillator to be found. Also called 124P37.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 37.0.1 132P37 [NB, 2010]
#C The second unique p37 oscillator to be found.
#C Unrelated to the other p37.
#C ----------------------------------------------------------------------
#C 39.0.0 P13-assisted P39 glider shuttle
#C ----------------------------------------------------------------------
#C 40.0.0 Beluchenko's p40 [NB 3/4/09]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C Two or four can hassle a blinker, for P80 and P160 respectively.
#C 40.0.1 [DRH 11/4/94]
#C A period 20+20 traffic light hassler. Period
#C 40/2, symmetry type "-c+e".
#C 40.0.2 [DJB before 5/91]
#C Period 40
#C 40.1.0 p40 traffic jam [NDE 10/14/94]
#C 40.1.1 P40 honey farm hassler
#C 40.2.0
#C Two Beluchenko's p40 hassling an I-heptomino and two blocks
#C Found in December 2020
#C ----------------------------------------------------------------------
#C 42.0.0 [MM, Oct 2014 (using JLS)]
#C (based on a period-doubling reaction by Dean Hickerson)
#C 42.0.1 P42 pulsar hassler
#C Contains two copies of the P21 traffic light hassler
#C Unlike pre-pulsar hasslers, this one becomes a full pulsar during
#C part of the cycle.
#C 42.1.0 P42 glider shuttle [RTW 9/84, MDN ??/94]
#C 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 P50 section) and 282+376n
#C (see 282.0.0), or by a larger p6 oscillator, giving period
#C 18 (see P18 section). 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 period 246), 230+40n
#C (see period 230), and 846+376n (not shown).
#C 42.1.1 P42 honey farm hassler
#C 42.1.2 P42 pre-pulsar hassler
#C ----------------------------------------------------------------------
#C 43.0.0 P43 Snark loop
#C Snarks can be used to make an oscillator of any period 43 or above.
#C The Snark was found by Mike Playle in 2013.
#C This particular loop can be made period 86, 172, or 344 by only
#C having 4, 2, or 1 glider present respectively.
#C Also see the period 54 section for the smallest 4-glider snark loop,
#C which has a smaller bounding box but only works for even periods >=54.
#C ----------------------------------------------------------------------
#C 44.0.0
#C P44 traffic light hassler
#C 44.0.1 P44 pre-pulsar shuttle
#C 44.1.0
#C P44 traffic light hassler
#C 44.1.1 [DJB 4/2/92, improved NDE 4/29/96]
#C 44.1.2 P44 glider gun [DJB 1997]
#C ----------------------------------------------------------------------
#C 45.0.0 P45 honey farm hassler
#C 45.0.1 Period-45 glider gun [MM 4/29/10]
#C A true period 45 glider gun (stabilized) found by Matthias Merzenich in 2010
#C with improvements by Adam P. Goucher, Dave Greene and Tanner Jacobi.
#C Same oscillator as the one stabilized by P9s. The still life shown in
#C three of the four ends is the smallest way to create the P45 oscillator.
#C 45.0.2 Period 45 glider shuttle
#C While it may look symmetric, its period is an odd number, so it can't be.
#C ----------------------------------------------------------------------
#C 46.0.0 Twin bees shuttle [RWG 1071]
#C 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. If only 1 block is used,
#C a large spark is produced which can reflect gliders and spaceships
#C in several ways. Also see periods 92, 138, 184, 230, 276, 690, and 40894.
#C 46.0.1 [DRH 10/26/94]
#C 2 shuttles push a beehive back and forth using 2 different reactions.
#C 46.1.0 P46 single-barrelled glider gun [RWG ???? {before 3/92}]
#C 46.1.1 Tanner's p46 [Tanner Jacobi]
#C A period 46 oscillator discovered by Tanner Jacobi in October 2017.
#C Unrelated to the twin bees shuttle
#C 46.1.2 P46 double-barrelled glider gun [RWG ???? {before 12/30/90}]
#C 46.2.0 p46 LWSS gun [RWG <=1992]
#C Based on a 135 degree glider -> LWSS reflection.
#C 46.2.1 p46 MWSS gun
#C Based on a 135 degree glider -> MWSS reflection from a pair of p46 shuttles.
#C 46.3.0 p46 LWSS loop [Peter Rott 11/93, PC 1994]
#C Based on a 90 degree LWSS reflection.
#C ----------------------------------------------------------------------
#C 47.0.0 [DJB#137 12/5/82]
#C Period 47
#C The highest prime period oscillator in this collection. However,
#C any period >=43, including primes, can be made using a simple
#C modification of the P43 snark loop.
#C ----------------------------------------------------------------------
#C 48.0.0 69P48 [NDE, 2002.]
#C The top part has period 16. The bottom part has period 7, but it skips a phase every 48 generations.
#C 48.0.1 65P48 [MM]
#C The smallest known period-48 oscillator, found 13 September 2014
#C 48.0.2 p48 pi hassler [MM, June 2011]
#C 48.1.0 [RTW 1995]
#C Sparks from 2 p12s move a pair of beehives.
#C 48.1.1 P48 traffic light hassler
#C 48.1.2 p48, type 2 toadflipper [RWG 12/11/94]
#C See discussion at period 60
#C 48.2.0 p48, type 2 toadsucker [RWG 12/11/94]
#C See discussion at period 60
#C ----------------------------------------------------------------------
#C 49.0.0 P49 bumper loop [Entity Valkyrie, 2018]
#C Smaller than the P49 Snark loop
#C ----------------------------------------------------------------------
#C 50.0.0 P50 traffic jam [NDE 10/16/93]
#C Period 50/2, symmetry type "n-e".
#C 50.0.1 #C 50.1.0 #C 50.1.1 P50 glider shuttle [DRH 3/19/92 (using early version of toaster)]
#C 2-glider shuttle with period 50+40n. See comments for P42 glider shuttle.
#C ----------------------------------------------------------------------
#C 51.0.0 Beluchenko's p51 [NB, 2/17/2009]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C ----------------------------------------------------------------------
#C 52.0.0 Four eaters hassling lumps of muck [DJB#119 10/1/77]
#C Period 52/4, symmetry type "nrc".
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 52.0.1 Four molds hassling eight blocks [NDE 2/21/95]
#C Period 52/4, symmetry type "nrk". 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 52.0.2 P52 R-pentomino hassler [NDE 3/19/96]
#C ----------------------------------------------------------------------
#C 54.0.0 P54 shuttle [DJB#62 <= 1976]
#C This is based on the twin bees shuttle
#C (period 46). Also see centinal (period 100).
#C 54.0.1 P54 snark loop
#C Any snark loop with period under 54 requires 8 gliders instead of 4,
#C increasing its size. The 4-glider version of the snark loop only
#C works for even periods. For period 54 specifically, the eaters in the
#C center would react with each other, so a single still life combining
#C the four eaters is needed.
#C See 43.0.0 for the 8-glider snark loop.
#C 54.0.2 Two P54 shuttles hassling pentadecathlon [DJB before 5/91]
#C ----------------------------------------------------------------------
#C 55.0.0 P55 traffic light hassler [DJB#162 1/26/86]
#C ----------------------------------------------------------------------
#C 56.0.0 P56 B-heptomino shuttle [DJB#162 1/26/86 (with Kok's Galaxy instead of blockers)]
#C LifeWiki says date of discovery unknown, so take the
#C date listed with a grain of salt
#C The smallest known period 56 oscillator
#C 56.0.1 Nonstandard p56 toadsucker [RWG 10/25/94]
#C 56.0.2 Nonstandard p56 toadflipper [RWG 1994]
#C 56.1.0 P56 traffic light hassler
#C ----------------------------------------------------------------------
#C 57.0.0 P57 bumper loop [Entity Valkyrie, 2018]
#C ----------------------------------------------------------------------
#C 58.0.0 Pre-pulsar shuttle 58 [Tanner Jacobi, 2015]
#C Period-58 oscillator with a 50% smaller population
#C than the previous Snark-based record.
#C 58.0.1 p58, type 3 toadsucker [RWG,MDN 10/25/94 (using larger p29s), DRH 12/13/94]
#C ----------------------------------------------------------------------
#C 60.0.0 [AF 7/18/94]
#C 2 p30 shuttles push a blinker up and down.
#C 60.0.1 [<= 1971]
#C P60 glider shuttle
#C 60.1.0 P60 boat-bit glider gun [1971?]
#C 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 15240.0.0.
#C 60.1.1 [NDE 5/30/98]
#C Pre-pulsar hassled by four caterers
#C 60.1.2 p60, type -1 toadsucker
#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 3", 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 period 58) or because the interaction with the spark is more
#C complicated (see period 56). Any oscillator that mentions
#C "see period 60" uses this mechanism. 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 60.1.3
#C p60, type 0 toadflipper
#C 60.2.0
#C p60, type 1 toadsucker
#C 60.2.1
#C p60, type 2 toadflipper
#C 60.2.2
#C p60, type 3 toadsucker
#C 60.2.3 Twirling T-tetsons II [RTW 1989]
#C Period 60/4, symmetry type "nrk".
#C 60.3.0 p60 traffic light hassler [NDE 12/2002]
#C Contains two copies of Karel's p15 and a heavyweight emulator (p4)
#C 60.3.1
#C P60 glider gun [V. Everett Boyer & Doug Petrie <=1973]
#C 60.3.2 Simkin's p60 [Michael Simkin, 2015]
#C The smallest known emu (Herschel tracks that are incapable of emitting gliders)
#C 60.4.0 p60 B-heptomino shuttle [Jason Summers and Noam Elkies in July 2003]
#C 60.4.1 Metamorphosis II [RTW 12/13/94]
#C 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 60.5.0 [NB 5/28/10]
#C ----------------------------------------------------------------------
#C 64.0.0 Merzenich's p64 [MM]
#C The smallest known period-64 oscillator.
#C 64.0.1 P64 thunderbird hassler [carybe, 2018]
#C Was discovered via symmetric soup search
#C 64.0.2 P64 pre-pulsar hassler
#C Contains two copies of Merzenich's p64 and half of 58.0.0.
#C 64.1.0 Four Merzenich's p64s hassling Octagon 2
#C Octagon 2 is period 5, but it skips a generation every time the p64s
#C give it sparks.
#C ----------------------------------------------------------------------
#C 70.0.0 78P70 [KS, 6/17/2007]
#C 70.0.1 [David I. Bell 6/1/02]
#C ----------------------------------------------------------------------
#C 72.0.0 Two blockers hassling R-pentomino [RTW 1990]
#C Looks identical but flipped after a half-cycle.
#C 72.0.1 p72 quasi-shuttle [Jason Summers, 2005]
#C 72.0.2 P72 traffic light hassler
#C ----------------------------------------------------------------------
#C 75.0.0 6 bits [RTW 9/84]
#C P75 glider shuttle. Named 6 bits because there are three domino sparks
#C that reflect the gliders.
#C ----------------------------------------------------------------------
#C 78.0.0 L156 [DJB 8/7/96]
#C Four of the eaters are used to turn the gun into an oscillator.
#C This oscillator can be made period 156, 312, or 624 by including only
#C 4, 2, or 1 Herschel.
#C ----------------------------------------------------------------------
#C 80.0.0 Two Beluchenko's p40s hassling blinker
#C ----------------------------------------------------------------------
#C 84.0.0
#C Period 84
#C Uses two unixes (P6) for stabilization.
#C ----------------------------------------------------------------------
#C 87.0.0 84P87 [Tanner Jacobi, 1/27/16]
#C The smallest known period-87 oscillator.
#C ----------------------------------------------------------------------
#C 88.0.0 P88 pi hassler
#C 88.0.1 P88 pre-pulsar hassler
#C 88.1.0 [RDH 1994]
#C P88
#C Based on P44
#C 88.1.1
#C ----------------------------------------------------------------------
#C 90.0.0
#C P90 pre-pulsar hassler
#C 90.0.1 #C 90.1.0 P90 glider gun [DRH]
#C 90.1.1 [FWKnightship 12/29/20]
#C P90 pre-pulsar hassler
#C 90.2.0 [DIB 11/30/93]
#C 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 periods 184 and 276.
#C 90.2.1
#C P90 glider shuttle
#C ----------------------------------------------------------------------
#C 92.0.0 P92 traffic light hassler
#C Contains an extra block that isn't part of the oscillator; this is
#C to provide better spacing for the next row.
#C 92.1.0 [DRH, NDE 1/15/95]
#C 2 p46 shuttles repeatedly reverse a loaf.
#C 92.1.1 [NDE 11/23/94]
#C 2 p46 shuttles push a blinker back and forth.
#C 92.1.2 [RTW 5/28/92]
#C 2 p46 shuttles push a beehive back and forth.
#C 92.1.3 P92 glider gun [DRH 1/7/91]
#C Made from 2 overlapping p46 guns.
#C 92.1.4 [RTW 3/91]
#C 2 p46 shuttles repeatedly convert blocks to gliders.
#C ----------------------------------------------------------------------
#C 94.0.0 P94 honey farm hassler
#C ----------------------------------------------------------------------
#C 96.0.0 P96 Hans Leo hassler [NDE 1/28/95]
#C A p12 sparker changes a traffic light into a B-heptomino; an
#C eater and a figure 8 change it back. Also see periods 132, 144, and 156.
#C 96.0.1
#C P96 traffic light hassler
#C ----------------------------------------------------------------------
#C 98.0.0 P98 emu
#C Based on R49 conduit discovered by Luka Okasnishi in 2019
#C Can be made period 196 by having only one R-pentomino
#C ----------------------------------------------------------------------
#C 100.0.0 Centinal [RWB before 9/87]
#C Based on P46 and P54 shuttles
#C 100.0.1 P100 traffic jam [NDE 10/15/94]
#C ----------------------------------------------------------------------
#C 102.0.0 Two Beluchenko's P51 hassling beehive
#C ----------------------------------------------------------------------
#C 104.0.0
#C Period 104
#C ----------------------------------------------------------------------
#C 106.0.0 [calcyman, March 2009]
#C Period 106
#C Minimum period oscillator possible with this stable reflector.
#C ----------------------------------------------------------------------
#C 108.0.0 P108, type 0 toadflipper
#C See discussion at period 60
#C 108.0.1 P108, type 1 toadsucker [DJB before 5/92]
#C See discussion at period 60
#C ----------------------------------------------------------------------
#C 110.0.0 P110 traffic jam [RWG 10/17/94]
#C There are also a P104 traffic jam with bounding box 594x132 and a
#C P102 with bounding box 577x85 that require different stabilization,
#C as fumarole and octagon 2 are P5. They are not shown here due to their large size.
#C 110.1.0 [KS 11/10/02]
#C Period 110, mod 55. Sparkers are period 5.
#C ----------------------------------------------------------------------
#C 112.0.0 L112 [DJB 7/5/96]
#C Four of the eaters (the ones on the edge of the bounding box) are used to
#C eat gliders and are not part of the conduit; if they were excluded, it
#C would be a 4-barreled gun.
#C Can be made P224 or 448 by including only one Herschel.
#C ----------------------------------------------------------------------
#C 120.0.0 P120 glider gun [DRH 1/13/91]
#C A blocker can convert a period 8n+4 glider gun to period 16n+8.
#C 120.0.1 P120 pre-pulsar hassler
#C 120.1.0 P120 HWSS gun
#C HWSSes cannot be eaten by eaters. They require other ways, such as
#C killer toads shown here. They are also harder to create; a glider hitting
#C a pre-block can create a LWSS or MWSS, but not a HWSS.
#C 120.2.0 P120 glider shuttle [MDN]
#C ----------------------------------------------------------------------
#C 122.0.0 L122
#C ----------------------------------------------------------------------
#C 124.0.0 P124 lumps of muck hassler
#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. Can be made into an agar.
#C ----------------------------------------------------------------------
#C 128.0.0 #C 128.0.1 [DJB before 11/91]
#C P128
#C 2 B-heptominoes move around a track of length
#C 256 gens formed from p8 oscillators. Also see 808.0.0.
#C ----------------------------------------------------------------------
#C 130.0.0 P130 shuttle [David Eppstein, 2001]
#C ----------------------------------------------------------------------
#C 132.0.0 P132 Hans Leo hassler [NDE 1995]
#C A p12 sparker changes a traffic light into a B-heptomino; a unix changes
#C it back. Also see periods 96, 144, and 156.
#C 132.0.1 [DJB before 8/94]
#C P132, based on P44
#C ----------------------------------------------------------------------
#C 133.0.0
#C Period 133
#C ----------------------------------------------------------------------
#C 135.0.0 [RWG 1989]
#C P135. A 2-glider shuttle, combining a rephaser and the
#C reflections from 75.0.0. Also see period 150.
#C ----------------------------------------------------------------------
#C 138.0.0 Gabriel's p138 [Gabriel Nivasch, 2002]
#C Appears mirrored after a half-cycle.
#C In its simplest form, it consists of only four octominoes (but not
#C the one simply called "octomino"), excluding dying sparks.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 138.0.1 P138 glider shuttle [RWG]
#C 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. The length of the loop may be
#C anything of the form 138+184n.
#C 138.0.2 P138 glider gun
#C ----------------------------------------------------------------------
#C 140.0.0
#C Period 140
#C ----------------------------------------------------------------------
#C 143.0.0 [Sphenocorona, 2020]
#C Uses two Bandersnatches and two 66P13s
#C ----------------------------------------------------------------------
#C 144.0.0 Achim's p144 [AF 7/21/94, DIB 8/8/94]
#C 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 Looks identical but flipped after a half-cycle.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 144.0.1 P144 glider gun
#C One of the four blocks is replaced with Rich's p16.
#C 144.0.2 P144 Hans Leo hassler [NDE 1/4/95]
#C A p12 sparker changes a traffic light into a B-heptomino; an eater changes
#C it back. Also see periods 96, 132, and 156.
#C ----------------------------------------------------------------------
#C 150.0.0 [DRH 1989]
#C Period 150
#C 150.0.1 [RTW <=1989]
#C A p150 2-glider shuttle, extensible to period 150+120N. Also see 165.0.0.
#C ----------------------------------------------------------------------
#C 156.0.0 P156 Hans Leo hassler [NDE 1/4/95]
#C A p12 sparker changes a traffic light into a B-heptomino; an eater changes
#C it back. Also see periods 96, 132, and 144.
#C 156.0.1 Jason's p156 [Jason Summers, 31 October 2004]
#C Oscillator, or actually an eight-barrelled glider gun,
#C discovered in a RandomAgar search. Also known as "92p156".
#C ----------------------------------------------------------------------
#C 160.0.0 Four Beluchenko's p40 hassling blinker
#C ----------------------------------------------------------------------
#C 165.0.0 P165 glider shuttle [RTW <=1989]
#C A p165 2-glider shuttle, extensible to period 165+120N.
#C ----------------------------------------------------------------------
#C 168.0.0 Pi orbital [NDE 8/22/95 with crowns, MM 4/6/10 with current oscillator]
#C Period 168, but can be made period 84 with two pi heptominoes
#C ----------------------------------------------------------------------
#C 177.0.0 Karel's p177 [KS, 2007]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C The highest-period known oscillator not made of multiple components
#C ----------------------------------------------------------------------
#C 180.0.0
#C P180 glider gun
#C Outputs 2 gliders consecutively per cycle
#C 180.0.1
#C P180 glider gun
#C Outputs 3 gliders consecutively per cycle
#C 180.0.2
#C P180 glider gun
#C Outputs 1 glider per cycle
#C ----------------------------------------------------------------------
#C 184.0.0 Period 184 glider gun [David Buckingham, 07/96]
#C Output suppressed
#C 184.0.1 P184 glider shuttle [DRH 1/24/92]
#C 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 period 276.
#C ----------------------------------------------------------------------
#C 188.0.0 P188 glider gun [RWG 10/16/94]
#C 188.0.1 Pseudo p94 gun [DJB,RCS,PC 7/11/94]
#C 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 ----------------------------------------------------------------------
#C 190.0.0 R190 [DJB 7/7/96]
#C Four copies of R190 Herschel track. Repeat time 107 ticks.
#C Can be made period 380 or 760 by including only 2 or 1 Herschel.
#C ----------------------------------------------------------------------
#C 200.0.0 P200 traffic jam [RWG 10/16/94]
#C ----------------------------------------------------------------------
#C 210.0.0 P210 glider gun
#C ----------------------------------------------------------------------
#C 225.0.0
#C Period 45 glider gun interacts with crystal; repeats every five gliders
#C 225.0.1
#C Uses two boojum reflectors, 180 degree reflector found in 2001 by Dave Greene
#C ----------------------------------------------------------------------
#C 226.0.0 P226 glider shuttle
#C Uses two boojum reflectors
#C ----------------------------------------------------------------------
#C 230.0.0 Obnoxious P230 [RWG 5/28/92]
#C Sparks from a p46 shuttle interact 3 times with sparks from a p5 MW volcano; one
#C interaction makes a temporary blinker; another makes a temporary glider.
#C 230.0.1 P230 glider shuttle [DRH 3/19/92 (using early version of toaster)]
#C 4-glider shuttle with period 230+40n. See comments for P42 glider shuttle.
#C 230.1.0 P230 glider gun [PC 6/28/94]
#C 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.
#C ----------------------------------------------------------------------
#C 240.0.0 P240 glider shuttle
#C ----------------------------------------------------------------------
#C 246.0.0 P246 bookend shuttle
#C Related to the P246 glider gun
#C 246.0.1 P246 glider shuttle [DRH 11/89 (p270+24n), 4/92 (p246)]
#C 2-glider shuttle with period 246+24n. See comments for P42 glider shuttle.
#C ----------------------------------------------------------------------
#C 270.0.0
#C Every 270 generations, a MWSS is created. However, it cannot
#C survive; the eater reaction is required for this to remain stable.
#C Without the glider eater at the bottom, it creates a cycle of 5 escaping,
#C 4 destroyed, repeating.
#C ----------------------------------------------------------------------
#C 276.0.0 P276 glider shuttle [DRH 1/24/92]
#C Glider shuttle based on the same reflection as in period 184. Also see period 90.
#C 276.1.0 4-barrelled p276 glider gun [DJB before 11/92]
#C 276.2.0 [NB, 11/9/10]
#C Contains two copies of Gabriel's p138
#C Is not the same halfway through the cycle, despite the period
#C being two P138 cycles.
#C The highest-period oscillator in this collection with volatility 1.
#C ----------------------------------------------------------------------
#C 282.0.0 P282 glider shuttle [RWG 9/13/92]
#C Based on P47. See comments for P42 glider shuttle.
#C ----------------------------------------------------------------------
#C 300.0.0 Period 300 glider gun
#C ----------------------------------------------------------------------
#C 312.0.0 60P312 [Dave Greene, 2004]
#C Based on Jason's p156
#C ----------------------------------------------------------------------
#C 360.0.0 P360 2-barrelled glider gun [DJB before 10/92]
#C ----------------------------------------------------------------------
#C 400.0.0 P400 glider loop [RWG 1987]
#C A glider bounces between 4 centinals. By expanding the loop and using more than one
#C glider, oscillators of period 100N can be built for any N.
#C ----------------------------------------------------------------------
#C 454.0.0
#C Period 454
#C Uses a boat-bit to double period
#C Can be made period 908 by including only one Herschel
#C ----------------------------------------------------------------------
#C 504.0.0
#C Period 504
#C ----------------------------------------------------------------------
#C 552.0.0 [RWG ????, DRH 1/23/92 ]
#C 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 that.
#C ----------------------------------------------------------------------
#C 690.0.0 [DRH 1/3/91]
#C 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]
#C A B-heptomino moves around a track made of various eaters and p8 oscillators; it makes
#C 4 moves each of durations 64, 65, and 73.
#C (In 1996, DJB found several B-heptomino moves using only
#C stable objects to form a track, thereby producing guns of 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]
#C Pseudo random number generator,
#C 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
#C RWG ????, DRH 1/10/95
#C Pseudo random 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. Moving the bottom
#C right gun and the reflector at the right edge 46N units
#C farther right changes the 10 above to K=10+4N (N>=0).
#C The period of the sequence depends on K as indicated in
#C the description of 15240.0.0.
Now I just have to finish the code to auto-generate LifeViewer labels for all of these objects, and append those comments to the above.