User:ColorfulGalaxy/List of polyominoes by apgcode

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A polyomino is a finite collection of orthogonally connected cells. This article lists polyominoes with up to 8 bits by apgcode.

Patterns

Haplominoes

There is only one haplomino, and by itself it dies after one generation. Several objects, such as the middleweight spaceship, produce dot sparks.

Pattern Apgcode Name Bounding box Perimeter of minimum covering convex polygon Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
xp0_1 Bit 1x1 4 1 1 0

Dominoes

There is also only one domino and by itself it too dies after one generation.

Pattern Apgcode Name Bounding box Perimeter of minimum covering convex polygon Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
xp0_3 Domino 1x2 6 2 1 0

Triominoes

There are exactly two distinct triominoes. Both of them have perimeter 8.

Pattern Apgcode Name Bounding box Perimeter of minimum covering convex polygon [note 1] Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
xp0_13 Pre-block 2x2 6+sqrt(2) 3.5 1 4
xp2_7 Blinker 1x3 8 3 0 3

Tetrominoes

There are five distinct tetrominoes.

Pattern Apgcode Name Perimeter Bounding box Perimeter of minimum covering convex polygon Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
xp0_17 Tail 10 2x3 7+sqrt(5) 5 3 6
xp0_27 T-tetromino 10 2x3 6+2*sqrt(2) 5 9 12
xs4_33 Block 8 2x2 8 4 0 4
xp0_36 Z-tetromino 10 2x3 6+2*sqrt(2) 5 2 6
xp0_f I-tetromino 10 1x4 10 4 2 6

Pentominoes

There are 12 distinct pentominoes. John Conway assigned them all letters in the range O to Z, loosely based on their shapes, and they are all shown below in order.

Pattern Apgcode Name Perimeter Bounding box Perimeter of minimum covering convex polygon Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
⠉⠇ xp0_117 V-pentomino 12 3x3 8+2*sqrt(2) 7 3 7
⠙⠆ xp0_136 W-pentomino 12 3x3 6+3*sqrt(2) 6.5 2 7
⠹⠁ xp0_171 T-pentomino 12 3x3 6+2*sqrt(5) 7 10 12
⠹⠂ xp0_172 R-pentomino 12 3x3 5+2*sqrt(2)+sqrt(5) 7 1103 116
⠹⠄ xp0_174 Z-pentomino 12 3x3 6+2*sqrt(5) 7 3 0
xp0_1f Q-pentomino 12 2x4 8+sqrt(10) 6.5 9 12
⠺⠂ xp0_272 X-pentomino 12 3x3 4+4*sqrt(2) 7 6 12
xp0_2f Y-pentomino 12 2x4 7+sqrt(2)+sqrt(5) 6.5 3 0
xp0_37 P-pentomino 10 2x3 8+sqrt(2) 5.5 4 0
xp0_3e S-pentomino 12 2x4 7+sqrt(2)+sqrt(5) 6.5 5 0
xp0_57 U-pentomino 12 2x3 10 6 4 0
..... xp0_v O-pentomino 12 1x5 12 5 6 12

Hexominoes

There are 35 distinct hexominoes, the majority of which behave uninterestingly. The most interesting and well-known examples are century, stairstep hexomino, table, toad and Z-hexomino.

Pattern Apgcode Name Perimeter Bounding box Perimeter of minimum covering convex polygon Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
⠉⡇ xp0_11f 14 3x4 9+sqrt(13) 9 4 4
⠙⠇ xp0_137 12 3x3 8+2*sqrt(2) 7 1 7
⠙⡆ xp0_13e (Lumps of muck) 14 3x4 7+sqrt(2)+sqrt(13) 8.5 67 16
⠩⠇ xp0_157 (Unknown reaction) 14 3x3 9+sqrt(5) 8 1102 116
⠹⠃ xp0_173 12 3x3 7+sqrt(2)+sqrt(5) 7.5 4 0
⠹⠅ xp0_175 14 3x3 9+sqrt(5) 8 9 0
⠹⠆ xp0_176 12 3x3 7+sqrt(2)+sqrt(5) 7.5 4 0
⠹⡄ xp0_17c 14 3x4 6+sqrt(2)+2*sqrt(5) 8.5 6 0
⢹⠁ xp0_1f1 (Unknown reaction) 14 3x4 6+2*sqrt(10) 9 176 55
⢹⠂ xp0_1f2 14 3x4 5+sqrt(2)+sqrt(5)+sqrt(10) 9 7 0
⢹⠄ xp0_1f4 14 3x4 5+sqrt(2)+sqrt(5)+sqrt(10) 9 5 0
⢹⡀ xp0_1f8 Z-hexomino 14 3x4 6+2*sqrt(10) 9 45 0
:.... xp0_1v 14 2x5 9+sqrt(17) 8 40 6
⠒⡇ xp0_22f 14 3x4 7+2*sqrt(2)+sqrt(5) 9 5 0
⠚⡆ xp0_23e (Lumps of muck) 14 3x4 6+4*sqrt(2) 9 67 16
⠺⠃ xp0_273 (Predecessor of the pond) 12 3x3 6+3*sqrt(2) 7.5 3 8
⠺⠅ xp0_275 (Common parent of the Pi-heptomino) 14 3x3 8+2*sqrt(2) 8 174 55
⠺⡄ xp0_27c Century (Parent of the bookend) 14 3x4 5+3*sqrt(2)+sqrt(5) 8.5 103 15
⢲⠃ xp0_2e3 14 3x4 5+3*sqrt(5) 9 3 0
⢺⠂ xp0_2f2 14 3x4 4+2*sqrt(2)+2*sqrt(5) 9 5 0
⢺⠄ xp0_2f4 14 3x4 4+2*sqrt(2)+2*sqrt(5) 9 1 6
.:... xp0_2v 14 2x5 8+sqrt(2)+sqrt(10) 8 4 4
⠓⡆ xp0_32e Ghost Herschel 14 3x4 7+2*sqrt(2)+sqrt(5) 9 6 0
⠳⡄ xp0_36c Stairstep hexomino 14 3x4 6+4*sqrt(2) 8 63 16
xp0_3f 12 2x4 9+sqrt(5) 7 2 5
⠚⠉⠁ xp0_3u 14 2x5 8+sqrt(2)+sqrt(10) 8 4 0
..:.. xp0_4v 14 2x5 8+2*sqrt(5) 8 9 12
xp0_5f 14 2x4 10+sqrt(2) 7.5 4 4
xp0_6f 12 2x4 8+2*sqrt(2) 7 3 4
xp0_77 Pre-beehive 10 2x3 10 6 1 6
xp0_7d 14 2x4 10+sqrt(2) 7.5 4 5
xp2_7e Toad 12 2x4 8+2*sqrt(2) 7 0 6
⠒⠋⠁ xp0_7s (Lumps of muck) 14 2x5 8+2*sqrt(5) 8 64 16
xp0_9f Table 14 2x4 12 8 15 0
…… xp0_vz1 △ 14 1x6 14 6 12 0

Heptominoes

There are 108 distinct heptominoes.

Pattern Apgcode Name Perimeter Bounding box Perimeter of minimum covering convex polygon Area of minimum covering convex polygon Lifespan in Conway's Life Final Population in Conway's Life
⠉⢹ xp0_111f (Unknown reaction) 16 4x4 10+3*sqrt(2) 11.5 36 12
⠉⢳ xp0_113e 16 4x4 8+4*sqrt(2) 11 6 7
⠉⢧ xp0_117c 16 4x4 7+3*sqrt(2)+sqrt(5) 10.5 18 24
⠉⡏ xp0_11f1 (Predecessor of the dot) 16 4x4 7+sqrt(10)+sqrt(13) 11.5 4 0
⠉⡗ xp0_11f2 (Predecessor of the MWSS spark) 16 4x4 6+sqrt(2)+sqrt(5)+sqrt(13) 11.5 4 0
⠉⡧ xp0_11f4 16 4x4 6+sqrt(2)+sqrt(5)+sqrt(13) 11.5 76 6
⠉⣇ xp0_11f8 F-heptomino 16 4x4 7+sqrt(10)+sqrt(13) 11.5 437 61
⠉⠉⠇ xp0_11v 16 3x5 10+2*sqrt(5) 11 4 8
⠙⢦ xp0_136c 16 4x4 6+5*sqrt(2) 9.5 177 32
⠙⡖ xp0_13e2 16 4x4 5+2*sqrt(5)+sqrt(13) 11 2 4
⠙⡦ xp0_13e4 (Unknown reaction) 16 4x4 5+3*sqrt(2)+sqrt(13) 10.5 34 12
⠙⣆ xp0_13e8 I-heptomino 16 4x4 6+sqrt(2)+sqrt(5)+sqrt(13) 10.5 247 39
⠉⠻ xp0_13f (Unknown reaction) 14 3x4 9+sqrt(13) 9 105 15
⠞⠉⠁ xp0_13u 16 3x5 8+sqrt(2)+2*sqrt(5) 10.5 5 0
⠩⡇ xp0_15f 16 3x4 9+sqrt(2)+sqrt(5) 9.5 18 6
⠹⢤ xp0_174c 16 4x4 6+2*sqrt(2)+2*sqrt(5) 11 5 7
⠹⠇ xp0_177 12 3x3 9+sqrt(5) 8 7 0
⠹⡤ xp0_17c4 H-heptomino 16 4x4 5+4*sqrt(2)+sqrt(5) 11 247 39
⠹⡅ xp0_17d 16 3x4 9+sqrt(2)+sqrt(5) 9.5 10 0
⠹⡆ xp0_17e (Unknown reaction) 14 3x4 7+2*sqrt(2)+sqrt(5) 9 66 16
⠉⠓⠆ xp0_17s (Glider predecessor) 16 3x5 7+3*sqrt(5) 10 4 5
⢉⡇ xp0_19f 16 3x4 10+sqrt(10) 10.5 23 24

Octominoes

Patterns Gallery

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Polyominoes tiling list (click above to open LifeViewer)


Notes

  1. The perimeter and area are calculated in Euclidean Geometry, where Euclidean distance is used. If you consider Manhattan distance instead of Euclidean distance, then the perimeter of the minimum covering convex polygon of the Herschel for example, would be 14 rather than 8+2*sqrt(5). (citation needed)

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