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oscillators.rle
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#N Oscillator stamp collection
#O Dean Hickerson, David Raucci, et al., updated Aug 15, 2024
#C A collection of 1738 oscillators of 211 different periods from 1
#C to 40894.
#C
#C Notes from Dean Hickerson:
#C The oscillators included here were found/built by many people over
#C many years. I finished putting the collection together in August 1995,
#C and have worked on this header file off and on since then. It's still
#C incomplete and probably inaccurate, but I've decided to make it public anyway.
#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://conwaylife.com/ref/lifepage/patterns/bhept/bhept.html
#C for Buckingham's description of this, and
#C https://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.
#C
#C Building this collection would have been impossible without the help
#C of many people. In addition to those who found the oscillators, I'd
#C like to thank Alan Hensel, Bill Gosper, Robert Wainwright,
#C Rich Schroeppel, and Jonathan Cooley for helpful suggestions, and
#C Andrew Trevorrow for writing LifeLab, an excellent Macintosh program
#C for building and running Life patterns. LifeLab's cross-platform
#C successor, Golly, is available as freeware at http://golly.sf.net .
#C
#C Dean Hickerson, [email protected]
#C 2/2/2000; last updated 9/16/2000. URLs corrected
#C and list of missing periods updated on 8/4/2023.
#C
#C Notes from David Raucci:
#C The 2013 discovery of the Snark allowed oscillators of all periods
#C 43 and higher. As of 7/21/23, all periods have been found, with
#C 41 being the last.
#C
#C If you find any errors or can fill in any of the blanks, please
#C let me know. This file has been updated from 2020 to 2024, converting it
#C to a Python program that automatically updates based on a text file input
#C and includes more oscillators that were not known in 1995.
#C
#C See the GitHub repository at https://github.com/dvgrn/b3s23osc for more
#C details.
#C
#C David Raucci, updated 8/15/24.
#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. Note that some of the symmetry types may no longer be
#C accurate after reductions.
#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 CC = Carson Cheng DIB = David Bell
#C DJB = David Buckingham DRH = Dean Hickerson
#C DER = David Raucci HH = Hartmut Holzwart
#C JHC = John Conway LJK = Luke Kiernan
#C KS = Karel Suhajda MDN = Mark Niemiec
#C MM = Matthias Merzenich mvr = Mitchell Riley
#C NB = Nicolay Beluchenko NDE = Noam Elkies
#C PC = Paul Callahan P1GG= Period1GliderGun
#C RTW = Robert Wainwright RCS = Rich Schroeppel
#C SN = Simon Norton RWG = Bill Gosper
#C
#C
#C JHC group = A group of people working with John Conway in the
#C early 1970s, including Conway, S. R. Bourne,
#C M. J. T. Guy, and Simon Norton.
#C MIT group = A group of people at MIT during the early 1970s,
#C including Robert April, Michael Beeler, Bill Gosper,
#C Richard Howell, Rici Liknaitzky, Bill Mann,
#C Rich Schroeppel, and Michael Speciner.
#C
#C Also, many of the common oscillators were found independently by many
#C people; this is indicated by an asterisk in the name field.
#C
#C Here are definitions of some terminology and notation used below; for
#C a more extensive glossary, see Stephen Silver's Life Lexicon, at
#C http://www.argentum.freeserve.co.uk/lex_home.htm
#C
#C The 'rotor' consists of all cells in an oscillator which change state.
#C The 'stator' consists of all cells which are alive in all generations.
#C (These terms were introduced by Allan Wechsler in 1994.)
#C
#C An oscillator whose stator is large is often called a 'billiard table';
#C such oscillators are somewhat easier to find than others, so many are
#C included in this collection.
#C
#C The 'period' of an oscillator (or spaceship) is the smallest positive
#C integer P for which generation P of the object is congruent to and in
#C the same orientation as generation 0. The 'mod' of an oscillator (or
#C spaceship) is the smallest positive integer M for which generation M
#C of the object is congruent to generation 0, but not necessarily in the
#C same orientation. The quotient q=P/M is always either 1, 2, or 4. To
#C specify both P and M, we often write "period P.M" or "period P/q".
#C
#C There are 43 types of symmetry that an oscillator can have, taking into
#C account both the symmetry of a single generation and the change of
#C orientation (if any) M generations later. There are 16 types of
#C symmetry that a pattern can have in a single generation. Each of these
#C is given a one or two character name, as follows:
#C
#C n no symmetry
#C
#C -c mirror symmetry across a horizontal axis through cell centers
#C -e mirror symmetry across a horizontal axis through cell edges
#C
#C / mirror symmetry across one diagonal
#C
#C .c 180 degree rotational symmetry about a cell center
#C .e 180 degree rotational symmetry about a cell edge
#C .k 180 degree rotational symmetry about a cell corner
#C
#C +c mirror symmetry across horizontal and vertical axes meeting
#C at a cell center
#C +e mirror symmetry across horizontal and vertical axes meeting
#C at a cell edge
#C +k mirror symmetry across horizontal and vertical axes meeting
#C at a cell corner
#C
#C xc mirror symmetry across 2 diagonals meeting at a cell center
#C xk mirror symmetry across 2 diagonals meeting at a cell corner
#C
#C rc 90 degree rotational symmetry about a cell center
#C rk 90 degree rotational symmetry about a cell corner
#C
#C *c 8-fold symmetry about a cell center
#C *k 8-fold symmetry about a cell corner
#C
#C For a period P/1 object, specifying the symmetry of generation 0 tells
#C us all there is to know about the oscillator's symmetry. For a period
#C P/2 or P/4 object, we also need to know how gen M is related to gen 0.
#C For the P/2 case, gen M can be either a mirror image of gen 0, a 180
#C degree rotation of it, or a 90 degree rotation of it if the pattern
#C has 180 degree rotational symmetry. For the P/4 case gen M must be a
#C 90 degree rotation of gen 0. In any case, if we merge all gens which
#C are multiples of M, the resulting pattern will have more symmetry than
#C the original oscillator. We describe the complete symmetry class of
#C the oscillator by appending the one or two character description of
#C the union's symmetry to that of gen 0's symmetry. For example, if
#C gen 0 has 180 degree rotational symmetry about a cell center, and
#C gen M is obtained by reflecting gen 0 across a diagonal, then the
#C union of gens 0 and M is symmetric across both diagonals, so its
#C symmetry class is denoted ".cxc".
#C
#C The 43 possible symmetry types are:
#C
#C period/mod = 1: nn -c-c -e-e // .c.c .e.e .k.k +c+c
#C +e+e +k+k xcxc xkxk rcrc rkrk *c*c *k*k
#C
#C period/mod = 2: n-c n-e n/ n.c n.e n.k
#C -c+c -c+e -e+e -e+k
#C /xc /xk
#C .c+c .cxc .crc .e+e .k+k .kxk .krk
#C +c*c +k*k xc*c xk*k rc*c rk*k
#C
#C period/mod = 4: nrc nrk
#C
#C The collection includes examples of all of these with mod=1, and many
#C with larger periods.
#C
#C ----------------------------------------------------------------------
#C
#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 and the period number after the percent sign.
#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 150 plus the digit width
#C or period >= 1000 with max bounding box expanding after generation 1000
#C are not supported unless the Python code is modified. ROW_WIDTH can be
#C changed at the top of the code to increase the allowed width above 150.
#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 1.0.0 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 section.
#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
#C and 15240.0.0 to convert a glider into a boat, which a
#C subsequent glider deletes.
#C Used as a rock in the conduit "Conduit 1" (aka BFx59H), as seen in
#C 78.0.0, 98.0.0, and 190.0.0.
#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 1.0.17 Long barge [JHC group 1970]
#C Still life frequency: 1 in 7,000
#C 1.0.18 Canoe
#C Also called sinking ship
#C Still life frequency: 1 in 200,000
#C 1.0.19 Shillelagh [Charles L. Corderman & Hugh Thompson 1971]
#C Still life frequency: 1 in 30,000
#C 1.0.20 Tub with tail [Charles L. Corderman & Hugh Thompson 1971]
#C Still life frequency: 1 in 125,000
#C 1.1.0 Hat
#C Found in 1971. Example of "-c" symmetry.
#C Still life frequency: 1 in 80,000
#C 1.1.1 Very long boat
#C Still life frequency: 1 in 100,000
#C Rarest still life with a 3-glider synthesis
#C 1.1.2 Long^3 snake
#C Rarest 9-bit still life, at 1 in 35M
#C 1.1.3 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 1.1.4 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 1.1.5 Cis-boat with tail
#C Still life frequency: 1 in 1.1M
#C 1.1.6 Long canoe
#C Still life frequency: 1 in 4M
#C 1.1.7 Long shillelagh
#C Still life frequency: 1 in 2.5M
#C 1.1.8 Tub with long tail
#C Still life frequency: 1 in 3M
#C 1.1.9 Long hook with tail
#C Still life frequency: 1 in 17.5M
#C 1.1.10 Very long ship
#C Still life frequency: 1 in 100,000
#C 1.1.11 Integral with hook
#C 1.1.12 Beehive with tail
#C Still life frequency: 1 in 500,000
#C 1.1.13 Cis-barge with tail
#C Still life frequency: 1 in 20M
#C 1.1.14 Claw with tail
#C Still life frequency: 1 in 4M
#C 1.1.15 Cis-hook with tail
#C 1.1.16 Loop
#C Still life frequency: 1 in 700,000
#C 1.1.17 Block on table
#C Still life frequency: 1 in 350,000
#C 1.2.0 Barge siamese loaf
#C Still life frequency: 1 in 20M
#C 1.2.1 Very long barge
#C Still life frequency: 1 in 8M
#C 1.2.2 Long^4 snake
#C 1.2.3 Long integral
#C Still life frequency: 1 in 3M
#C 1.2.4 Boat with long tail
#C Still life frequency: 1 in 2.25M
#C 1.2.5 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 1.2.6 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 1.2.7 Trans-barge with tail
#C Still life frequency: 1 in 6M
#C 1.2.8 Fuse with two tails
#C 1.2.9 Boat-tie
#C Pun on bowtie
#C Still life frequency: 1 in 30,000
#C 1.2.10 Very long canoe
#C 1.2.11 Snake siamese snake
#C 1.2.12 Carrier siamese snake
#C Also called broken snake
#C Still life frequency: 1 in 2M
#C 1.2.13 Carrier siamese carrier
#C Still life frequency: 1 in 20M
#C 1.2.14 Tub with very long tail
#C 1.2.15 Very long shillelagh
#C Still life frequency: 1 in 18M
#C 1.2.16 Very long hook with tail
#C 1.2.17 Table and table
#C Still life frequency: 1 in 150,000
#C 1 in 10,000 in D2 symmetry (reflection)
#C 1.2.18 Moose antlers
#C Still life frequency: 1 in 300,000
#C 1.3.0 Twin hat
#C Still life frequency: 1 in 600,000
#C 1.3.1 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 1.3.2 Fourteener
#C Still life frequency: 1 in 700,000
#C 1.3.3
#C Example of "+c" symmetry
#C 1.3.4 Honeycomb
#C Much more common in rules with S8, as a line of six becomes a honeycomb
#C 1.3.5 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 1.3.6 Paperclip
#C Still life frequency: 1 in 14,000
#C 1.3.7 Big S
#C Still life frequency: 1 in 30,000 [MIT group 1971]
#C 1.3.8 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 1.3.9 Block on dock
#C Still life frequency: 1 in 400,000
#C 1.3.10 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 1.3.11 Cap and table
#C Example of "-e" symmetry
#C 1.3.12 Half-bakery
#C As its name would suggest, they often appear in pairs.
#C Still life frequency: 1 in 1250
#C 1.3.13 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 1.3.14 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 1.3.15 Beehive on dock
#C Still life frequency: 1 in 300,000
#C 1.3.16 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 1.4.0 Spiral [RTW 1971]
#C Example of "rc" symmetry
#C 1.4.1 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 1.4.2
#C Example of "+k" symmetry
#C 1.4.3
#C Example of "rk" symmetry
#C 1.4.4 7x9 eater
#C See P22, P25, and P94 sections.
#C 1.4.5 31.4 [Mike Playle, 2013]
#C Used in the Snark, which is probably the most important discovery in the 2010s.
#C 1.4.6 O quad loaf
#C Still life frequency: 1 in 27.5M; very common for 28 bits
#C 1.4.7 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 1.4.8 Eater 4 [DJB]
#C See the period 9, 11, 29, 30, and 58 sections for the eater 4 in action.
#C 1.4.9 [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, 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 2.0.12
#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 2.0.13 Why not [DJB 7/77]
#C 2.0.14
#C 2.1.0 Eater plug [RTW 2/73]
#C 2.1.1 Piston [* 1971]
#C Example of "-c+c" symmetry.
#C 2.1.2
#C Example of "-c+c" symmetry.
#C 2.1.3 Quad [Robert A. Kraus 4/71]
#C Example of "rk*k" symmetry.
#C 2.1.4
#C Example of "-c+e" symmetry.
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 2.1.5 Blinkers bit pole [RTW 6/77]
#C Example of "n.e" symmetry.
#C 2.1.6 [DRH 5/20/93]
#C Example of "n.k" symmetry.
#C 2.1.7 [DRH 5/20/93]
#C Example of "n.k" symmetry.
#C 2.1.8 Washing machine [RTW before 6/72]
#C Example of "xc*c" symmetry.
#C 2.1.9 Block on griddle [RTW 7/72]
#C Can be stabilized other ways
#C Example of "n-e" symmetry.
#C 2.1.10 [DRH 5/20/93]
#C Example of "n-c" symmetry.
#C 2.2.0 [DRH 5/20/93]
#C Example of "n/" symmetry.
#C 2.2.1 Laputa [RCS 9/23/92]
#C Example of "n.e" symmetry.
#C 2.2.2 [DRH 5/20/93]
#C Example of "n.c" symmetry.
#C 2.2.3 Fore and back [AF 7/12/94]
#C Example of ".c+c" symmetry.
#C 2.2.4 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 2.2.5 Skewed quad
#C A period 2 oscillator and muttering moat.
#C 2.2.6 Spark coil [* 1971]
#C Usually formed by two pi heptominoes facing each other four cells apart.
#C Oscillator frequency: 1 in 15M
#C 2.2.7 Four boats
#C 2.2.8 [DRH 4/23/93]
#C Example of ".k+k" symmetry.
#C 2.2.9 [DRH 1994]
#C Infinitely extensible
#C 2.2.10 Light bulb [* 1971]
#C 2.3.0
#C Variant of light bulb
#C 2.3.1 Almosymmetric [* 1971]
#C Example of "n-e" symmetry.
#C 2.3.2 [DRH 4/23/93]
#C Example of ".c+c" symmetry.
#C 2.3.3 Example of ".cxc" symmetry.
#C 2.3.4 [DRH 4/23/93]
#C Example of "/xc" symmetry.
#C 2.3.5 [AWH 8/25/94]
#C Infinitely extensible
#C 2.3.6
#C Example of ".kxk" symmetry.
#C 2.3.7 [DRH 1973]
#C Example of "-e+e" symmetry. Infinitely extensible.
#C 2.3.8 [DRH 4/23/93, stator since improved]
#C Example of "-e+e" symmetry.
#C 2.4.0 [DRH 4/23/93]
#C Example of "-e+e" symmetry.
#C 2.4.1 [DRH 4/23/93]
#C Example of "-e+k" symmetry.
#C 2.4.2 [DRH 1994]
#C Infinitely extensible
#C 2.4.3 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 2.4.4 [DRH 4/23/93]
#C Example of ".crc" symmetry.
#C 2.4.5 [AF 7/26/94]
#C Example of "rk*k" symmetry. A muttering moat.
#C 2.4.6
#C Example of ".e+e" symmetry.
#C 2.4.7
#C Example of "+k*k" symmetry.
#C 2.5.0 [DRH 4/23/93]
#C Example of "rc*c" symmetry.
#C 2.5.1 [DRH 4/23/93]
#C Example of "xk*k" symmetry.
#C 2.5.2 [DRH 1994]
#C Infinitely extensible
#C 2.5.3
#C Example of "+k*k" symmetry.
#C 2.5.4 [RTW <1990]
#C Infinitely extensible
#C 2.5.5
#C Example of "xk*k" symmetry.
#C 2.6.0
#C Example of ".krk" symmetry.
#C 2.6.1 [RTW <1990]
#C Infinitely extensible
#C 2.6.2 [bottom end: RTW <1990; top end: DRH 1995]
#C Infinitely extensible
#C 2.6.3 [RTW <1990]
#C Infinitely extensible
#C 2.6.4 [Agar found by Robert A. Kraus 1971, stabilized by ????]
#C 2.6.5 [DRH 1994]
#C Infinitely extensible
#C 2.7.0 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 2.7.1 Squaredance [Agar found by Don Woods, 1971, stabilized by DRH 3/25/93]
#C 2.7.2 [Agar found by Robert A. Kraus 1971, stabilized by DRH 12/13/94]
#C 2.7.3
#C 2.8.0 Houndstooth agar [DRH 3/30/94]
#C 2.8.1 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 2.8.2 [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 Candlefrobra [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 3.0.7 [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 3.1.0 [RTW 11/84]
#C DRH calls this Candlefrobra, which is now used to refer to a different
#C period-3 oscillator.
#C 3.1.1 2 eaters [RWG 9/71]
#C 3.1.2 Cuphook [RCS 10/70]
#C 3.1.3 Stillater [RTW 9/85]
#C 3.1.4 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 3.1.5
#C 3.1.6 [NB, Dec 2012]
#C 3.1.7 [NB, Dec 2012]
#C 3.2.0 Caterer [DRH 8/4/89]
#C Provides a spark used in other oscillators
#C 3.2.1 Pulsar quadrant [DJB#46 7/73]
#C 3.2.2 1-2-3 [DJB#4 8/72]
#C 3.2.3 [AF 8/22/94, stator since reduced]
#C 3.2.4 Loading dock [DJB#3 9/72]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.2.5 Snake dance [RTW 5/72]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.2.6 New five [DRH 1/90]
#C 3.2.7 [DJB#92 7/26/76]
#C 3.2.8 Surprise [DJB#10 11/72]
#C 3.3.0 [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 3.3.1 Eaters plus [RTW 7/91]
#C Also called French kiss
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.3.2 Two pulsar quadrants [DJB#47 7/73]
#C 3.3.3 [RTW 4/82]
#C 3.3.4 Germ [DJB#9 9/72]
#C 3.3.5 Mini pressure cooker [RTW before 6/72]
#C 3.3.6 Cross [RTW 10/89]
#C One of the few known oscillators in which one phase is a polyomino.
#C 3.4.0 Runny nose [83bismuth38, 2017]
#C 3.4.1 [NB, Jan 2013]
#C 3.4.2 [NB, Jan 2013]
#C 3.4.3 Fire-spitting [NB, 09/2003]
#C 3.4.4 [DJB#7 <=1976]
#C Same rotor as in "2 eaters".
#C 3.4.5 [RTW 6/72]
#C 3.4.6 Triple caterer [DRH 8/89]
#C 3.4.7 [DRH 1/90]
#C Smallest known p3 (as of 1995) in which a corner of the
#C bounding box is active.
#C 3.4.8 [NB, Jan 2013]
#C 3.4.9 [NB, Jan 2013]
#C 3.4.10 [NB, Jan 2013]
#C 3.5.0 [NB, 2013?]
#C 3.5.1 Snake pit 2
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.5.2 Biting off more than they can chew [Peter Raynham 7/72]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.5.3 Pressure cooker [MIT group 9/71]
#C 3.5.4 Hustler [RTW 6/71]
#C 3.5.5 Double caterer [DRH 8/89]
#C 3.5.6 P3 rumbling river [DRH 11/26/94]
#C The rotor is connected and contained in a strip of height 2.
#C 3.6.0
#C 3.6.1 [NB, Jan 2013]
#C 3.6.2 Tubber [RTW before 6/72]
#C Rotor is confined to 2 parallel diagonals.
#C 3.6.3 Diamond ring [DJB#2 1972]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 3.6.4 [RTW 8/89]
#C 3.6.5 [AF 7/30/94 (symmetric form)]
#C 3.6.6 Star [HH 2/16/93]
#C Another polyomino.
#C 3.6.7 [HH 3/5/93]
#C Any of its four corners can be present or absent, and it will still work
#C 3.7.0 [DRH 9/18/89]
#C 3.7.1 [DRH 8/89]
#C 3.7.2 [DRH 8/89]
#C 3.7.3 2x3 cross [HH 2/26/93]
#C A larger version of Cross, which may be made any size.
#C 3.7.4 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 3.7.5 [HH 3/5/93]
#C 3.7.6 Trans-skewed pulsar quadrants
#C 3.8.0 [DRH 1994]
#C 3.8.1 [DJB#103 6/3/77]
#C Rotor has symmetry type "-c", but stator can't be made symmetric.
#C 3.8.2 [DRH 10/89]
#C 3.8.3 Double ewe [RTW before 9/71]
#C 3.8.4 Skewed traffic light [RTW 8/89]
#C Uses two caterers and two jams, but could just as easily use four of either
#C 3.8.5 [DRH 11/27/94]
#C 3.9.0
#C 3.9.1 [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 3.9.2 [DRH 11/27/94]
#C 3.9.3 [RWG 9/22/94]
#C 3.10.0 Statorless P3 [Jason Summers, 2012]
#C This oscillator was the first discovered P3 to have volatility 1
#C 3.10.1 Quasar [RTW 8/71]
#C 3.10.2 [DIB 3/7/93]
#C 3.11.0
#C Period 3 agar
#C 3.11.1
#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 4.0.6 Heavyweight emulator [RTW 6/80]
#C Supplies a domino spark
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.0.7 [JS]
#C 4.1.0 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 4.1.1 Tempest [DRH 8/89]
#C Period 4/2, symmetry type "/xk".
#C 4.1.2 20P4 [DRH before 4/92]
#C 4.1.3 24P4.1 [DRH 9/89]
#C Statorless.
#C 4.1.4 [DJB#104 6/3/77]
#C Babbling brook
#C 4.1.5 [DRH 8/89]
#C 4.1.6 [DJB#98 4/28/77]
#C Period 4/2, symmetry type "n-e".
#C 4.2.0 [DRH 10/89]
#C Related to the P60 toad hasslers.
#C 4.2.1 [DRH ????, DIB 12/11/94]
#C 4.2.2
#C 4.2.3 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 4.3.0 [DRH 3/90]
#C Period 4/2, symmetry type "n/".
#C 4.3.1 [DRH 3/90]
#C Period 4/2, symmetry type "n/".
#C 4.3.2 [DRH 3/90]
#C Period 4/2, symmetry type "n/".
#C 4.3.3 Jack [RTW 4/84]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 4.3.4 Ellison p4 HW emulator hybrid [Scot Ellison, April 2010]
#C A period 4 oscillator that produces a domino spark.
#C 4.3.5 Eater/block frob [DJB#51 <=1976]
#C 4.3.6 [DRH 11/10/94]
#C Babbling brook
#C 4.3.7 [DRH 8/89]
#C Period 4/2, symmetry type "n-e".
#C 4.3.8 [DRH 8/89]
#C Period 4/2, symmetry type "n-e".
#C 4.4.0 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 4.4.1 [DJB#20 <1977]
#C 4.4.2 [DRH 12/10/94]
#C 4.4.3 [DRH 8/89, AF 1994]
#C 4.4.4 Confused eaters [DJB#49 before 1973]
#C Period 4/2, symmetry type "n/".
#C 4.4.5 [DJB#13 before 1973]
#C Babbling brook. Period 4/2, symmetry type "n/".
#C 4.4.6 [AF 7/17/94 (symmetric form), RWG,AWH 11/20/94]
#C 4.4.7 [RTW 11/90]
#C 4.5.0
#C 4.5.1 [12/6/94]
#C 4.5.2 [???? 1971]
#C 4.5.3 [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 4.5.4 [MM, Oct 2013 (using WLS)]
#C (possibly known earlier)
#C 4.6.0 Purveyor [83bismuth38 1/26/22]
#C Provides a spark similar to caterer, but it's p4, not p3
#C An example of purveyor in action can be seen in the p28 section.
#C 4.6.1 [DJB#23 <1973?]
#C 4.6.2 Pinwheel [SN 4/70]
#C Period 4/4, symmetry type "nrk".
#C 4.6.3 Clock II
#C Period 4/4, symmetry type "nrk".
#C 4.6.4 T-nosed P4 [RTW 1989]
#C Featured prominently in several P36 oscillators, as well as P8, 16, 44, 52, and 56.
#C 4.6.5 [DRH 8/89]
#C Period 4/2, symmetry type "n-C".
#C 4.6.6 [DJB#21 <1973]
#C 4.6.7 [DRH 12/10/94]
#C 4.6.8 [DRH 7/14/94]
#C 4.7.0 [DRH 4/6/92]
#C 4.7.1
#C Lightweight variant, also exists in middleweight and heavyweight variants
#C 4.7.2
#C A narrower but longer T-nosed p4
#C 4.7.3 Wavefront [DJB#24 <= 1976]
#C Rotor is confined to 2 parallel diagonals.
#C 4.7.4 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 4.7.5 [AF, AWH, DRH, 1994]
#C Only 3 cells are p4; the rest are p1 or p2.
#C 4.7.6 [AF 8/31/94 (symmetric form)]
#C 4.7.7 [DJB#69 <=1976]
#C 4.7.8 [DRH 12/10/94]
#C 4.8.0 Overweight emulator [RTW ????]
#C 4.8.1 [AWH 2/10/95]
#C 4.8.2 T-nosed P4 variant [Entity Valkyrie]
#C 4.8.3 [DJB#28 before 1973?]
#C Rotor is p4/2, symmetry type "rk*k".
#C 4.8.4 Boss [DJB#30 1972]
#C 4.8.5 [DRH 12/10/94]
#C 4.8.6 Butter [Entity Valkyrie]
#C 4.8.7 [AF 8/23/94 (symmetric form)]
#C 4.9.0 [DRH 12/10/94]
#C 4.9.1
#C 4.9.2 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 4.9.3 [RTW 9/89]
#C 4.9.4 [AF 7/13/94]
#C May be compressed horizontally by 1 or 2 cells.
#C 4.9.5 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 4.10.0 [RTW 9/91]
#C 4.10.1 [DRH 1/10/95]
#C Period 4/4, symmetry type "nrc".
#C 4.10.2
#C 4.11.0 Windmill [DRH 11/89]
#C 4.11.1 [RTW ????, AF 8/7/94]
#C An octagon of side 2, showing 2 ways to stabilize the edge.
#C 4.11.2 [MM, Jan 2011]
#C (based on a sparker by Noam Elkies)
#C 4.11.3 [RTW before 10/92]
#C The molds can be replaced by middleweight emulators.
#C 4.11.4 [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 4.11.5 [DRH 1/10/95]
#C Period 4/4, symmetry type "nrc".
#C 4.11.6 [DRH 9/89]
#C An octagon of side 3, showing 4 ways to stabilize the edge.
#C 4.12.0 [DRH,RTW 9/89, AF 8/7/94]
#C An octagon of side 5, showing 4 ways to stabilize the edge.
#C 4.12.1 Sixty-nine [RTW 10/78]
#C Period 4/4, symmetry type "nrk".
#C 4.12.2
#C 4.12.3 [RTW 9/89 ]
#C Period 4/2, symmetry type ".crc".
#C 4.12.4 [DRH 1994]
#C 4.13.0 [DRH]
#C Period 4/2, symmetry type "+k*k".
#C 4.13.1 [DIB,DRH 12/12/94]
#C 4.13.2 [DRH 1994]
#C 4.13.3 [DRH 9/16/92]
#C Stabilized p4 agar, made of several parallel lines.
#C 4.13.4 [RTW 9/91, DRH 1/14/95]
#C First stabilization (not shown here) was found by RTW 9/91.
#C 4.14.0 Strictly volatile p4 [Dongook Lee 11/18/21]
#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 There is also an unusual catalysis that can be seen in 45P25.
#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 5.0.8 Hooks
#C Uses a catalyst that's also used in 28P7.2.
#C Related to pentant in a different way.
#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 5.1.5 [DJB#160 1/6/87]
#C 5.2.0 [DJB#101 5/2/77]
#C 5.2.1 [DJB#44]
#C 5.2.2 Pedestle [DJB#39 1973]
#C Contains two copies of the rotor in technician
#C 5.2.3 Pseudo-barberpole [AF 8/22/94]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.2.4 [RTW 1/82 (DJB#146)]
#C 5.2.5 Pentant [DJB#85 7/11/76]
#C Also see hooks, which is also period 5.
#C 5.2.6 101 [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 5.2.7 Siesta [DJB#57 1973]
#C 5.3.0 [DJB#84 7/76?]
#C 5.3.1 [AF 7/27/94]
#C 5.3.2 aVerage [DJB#35 1973]
#C 5.3.3 Middleweight volcano [DRH 4/6/92]
#C Supplies sparks that are used in some oscillators of
#C periods 20, 25, 30, 125, and 230.
#C 5.3.4 Chemist [DJB#38 1973]
#C 5.3.5 [DJB#87 7/15/76]
#C 5.3.6 Pentoad [RWG 6/77]
#C Has appeared semi-naturally (i.e. from symmetric soup)
#C 5.3.7
#C Based on the pseudo-barberpole
#C 5.4.0
#C The basis of the P17 and P27 phase change oscillators.
#C 5.4.1 P5 pipsquirter [Dongook Lee, 2018]
#C A pipsquirter is an oscillator that emits a 1x2 spark vertically.
#C 5.4.2 [AF 7/13/94]
#C 5.4.3 [DJB#158 2/25/85]
#C 5.4.4 [DRH 1994]
#C 2 fumaroles hassle a long barge.
#C 5.4.5 [AF 8/7/94 (symmetric form), AWH 11/19/94]
#C 5.4.6 Toaster [DRH 4/1/92]
#C 5.4.7 [DJB#142 5/21/84]
#C 5.5.0 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 5.5.1 [Gabriel Nivasch 10/23/02]
#C 5.5.2 [11/19/94]
#C Also works even if the right part is not shifted two cells
#C 5.5.3 [DJB#151 9/29/84]
#C Optimized for bounding box, not for population