List of common evolutionary sequences
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In late 2016, Simon Ekström determined the most common evolutionary sequences using 8 × 8 random soups.[1]
To qualify on the list, a pattern must initially have 12 or fewer cells and reach 20, staying above 12 for at least four generations with different population, at some point in its evolution. For this reason, the traffic light and interchange do not qualify.
| Sequence | Pattern | Lifespan[n 1] | Final population | Census | Occurrences | Rel. freq. |
|---|---|---|---|---|---|---|
| Honey farm predecessor (bun shown) |
17 | 24 | 4 beehives | 617733[n 2] | 1.000 | |
| R-pentomino | 1103 | 116 | 8 blocks 6 gliders 4 beehives 4 blinkers 1 boat 1 ship 1 loaf |
531779 | 0.861 | |
| Pi-heptomino | 173 | 55 | 6 blocks 5 blinkers 2 ponds |
471544 | 0.763 | |
| Lumps of muck | 63 | 16 | 4 blocks | 310237 | 0.502 | |
| Century | 103 | 15 | 3 blocks 1 blinker |
266004[n 3] | 0.430 | |
| B-heptomino | 148 | 28 | 3 blocks 2 gliders 1 ship |
244984[n 4] | 0.397 | |
| Wing | 104 | 9 | 1 block 1 glider |
133659 | 0.216 | |
| Herschel with block (B-heptomino descendant) |
128 | 28 | 3 blocks 2 gliders 1 ship |
121316 | 0.196 | |
| Teardrop | 20 | 8 | 2 beehives | 64485 | 0.104 | |
| I-heptomino | 247 | 39 | 3 blocks 2 gliders 1 boat 1 beehive 1 ship |
53177 | 0.086 | |
| Two-glider octomino | 385 | 48 | 8 blinkers 4 beehives |
50178 | 0.081 | |
| Long bun | 53 | 12 | 3 blocks | 48239 | 0.078 | |
| Procrastinator [2][3] | 73 | 6 | 1 beehive | 46879 | 0.076 | |
| Blonk-tie | 552 | 104 | 8 blocks 2 boats 2 gliders 2 beehives 2 ship-ties 1 blinker 1 ship 1 loaf |
38554 | 0.062 | |
| Iwona active region | 238 | 33 | 3 blinkers 2 blocks 1 boat 1 glider 1 beehive |
37747 | 0.061 | |
| U-turner[4] | 163 | 16 | 4 blinkers 1 block |
29273[n 5] | 0.047 | |
| Herschel descendant hassled in period-184 glider gun, H' (without its first natural glider) |
106 | 19 | 2 blocks 1 glider 1 ship |
29196 | 0.047 | |
| R-turner[5] | 268 | 45 | 5 blocks 3 blinkers 2 gliders 1 ship |
28314 | 0.046 | |
| Original diehard | 130 | 0 | 27077 | 0.044 | ||
| Object hassled in Jason's p22 | 65 | 17 | 1 block 1 beehive 1 loaf |
25303 | 0.041 | |
| Traffic light hitting block (creating block and blinker) |
47 | 7 | 1 blinker 1 block |
24725 | 0.040 | |
| Dove | 200 | 18 | 3 blocks 2 blinkers |
23603 | 0.038 | |
| Unnamed (soon evolves into a pi and loaf) (evolves from o3bo$ob3o$6bo) |
354 | 71 | 10 blinkers 5 blocks 2 boats 1 glider 1 ship |
22654 | 0.0367 | |
| Herschel (by itself) | 128 | 24 | 2 blocks 2 gliders 1 ship |
21929[n 6] | 0.0355 | |
| Butterfly | 33 | 12 | 2 beehives | 18593 | 0.0301 | |
| Octomino II | 116 | 20 | 2 blinkers 2 blocks 1 ship |
18507[n 7] | 0.0300 | |
| Traffic light hitting block, leaving single beehive | 69 | 6 | 1 beehive | 17795 | 0.0289 | |
| Traffic light hitting block, leaving two blinkers | 36 | 6 | 2 blinkers | 17656 | 0.0286 | |
| Object hassled in Karel's p177 | 153 | 12 | 1 block 1 pond |
17620 | 0.0285 | |
| Unnamed | 18 | 0 | 17007 | 0.0275 | ||
| Object hassled in Merzenich's p64 | 34 | 6 | 1 beehive | 16764 | 0.0271 | |
| Unnamed | 45 | 21 | 7 blinkers | 16695 | 0.0270 | |
| Traffic light hitting block | 173 | 20 | 1 blinker 1 block 1 toad 1 loaf |
16414 | 0.0266 | |
| A single unit in the 3c/7 wave (evolves into U-turner descendent and a beehive) |
27 | 0 | 16361 | 0.0265 | ||
| Traffic light hitting block | 211 | 45 | 3 beehives 2 blocks 2 loaves 1 glider |
15854 | 0.0257 | |
| Clean bi-block predecessor | 44 | 8 | 2 blocks | 15621 | 0.0253 | |
| Traffic light hitting block | 22 | 9 | 3 blinkers | 15505 | 0.0251 | |
| Lumps of muck hitting block | 83 | 17 | 2 blocks 1 blinker 1 beehive |
15475 | 0.0251 | |
| Intermediate generation of octomino II | 94 | 20 | 2 blinkers 2 blocks 1 ship |
14689 | 0.0251 | |
| Unnamed six-cell pattern listed as 5.s.1[6] | 49 | 19 | 2 beehives 1 loaf |
14585 | 0.0236 | |
| Unnamed beehive edge-shooter[n 8] | 61 | 6 | 1 beehive | 14525 | 0.0235 | |
| Flare | 49 | 0 | 14509 | 0.0235 | ||
| Flop | 17 | 8 | 1 blinker 1 boat |
13997 | 0.0227 | |
| Unnamed methuselah making procrastinator and beehive | 1675 | 273 | 17 blinkers 16 blocks 12 beehives 8 gliders 3 loaves 2 ships 1 boat 1 pond |
13661 | 0.0221 | |
| Active reaction that can be turned into an anvil via the interaction of anything that can act as a boat-bit. | 320 | 41 | 4 blinkers 3 blocks 1 boat 1 glider 1 long boat |
13484 | 0.0218 | |
| Unnamed; pi-heptomino hitting boat[n 9] | 124 | 14 | 2 blocks 1 beehive |
12411 | 0.0201 | |
| U-turner 30-generation predecessor | 193 | 16 | 4 blinkers 1 block |
12200 | 0.0197 | |
| Unnamed | 62 | 8 | 1 block 1 tub |
11929 | 0.0193 | |
| AK-47 reaction | 252 | 58 | 3 blocks 3 gliders 3 beehives 2 blinkers 1 loaf |
11426 | 0.0185 | |
| B-heptomino predecessor | 155 | 28 | 3 blocks 2 gliders 1 ship |
11287 | 0.0183 | |
| Late generation of original diehard | 57 | 0 | 11197 | 0.0181 | ||
| Pi + block[n 10] | 1235 | 291 | 29 blocks 13 blinkers 7 gliders 5 beehives 3 ships 2 tubs 2 loaves 2 ship-ties 1 long boat |
11054 | 0.0179 | |
| E-heptomino cousin[n 11] | 361 | 52 | 5 blocks 4 beehives 1 blinker 1 glider |
11035 | 0.0179 | |
| Honey farm + block | 36 | 11 | 1 glider 1 beehive |
10747 [n 12] | 0.0174 | |
| Unnamed | 26 | 3 | 1 blinker | 10467 | 0.0169 |
Of the top 96, the queen bee ranks 81st (7910 occurrences), and the pulsar ranks 86th (7360 occurrences).[n 13] The F-heptomino (5154 occurrences), thunderbird (6161 occurrences), and switch engine (687 occurrences) do not make the top 96. The Z-hexomino ranks 146th (4675 occurrences). Other patterns of note that are more common than the switch engine include multum in parvo (3404), one of the less familiar fours, four blocks in a rectangle (1615), the sequence that forms from a row of 8 on cells (1434), the active reaction in the p130 shuttle (1126), a clean paperclip (1053), gliders by the dozen (855), and a clean bipond (830).
This census for small, common active reactions may provide insights into finding bottlenecks for new conduits.
Common enough but not large enough
This list is more subjective, since these objects do not qualify as large enough. The number of three-glider collisions and the number of octohash collisions can provide a rough estimate. These are not guaranteed to be in order of frequency.
| Sequence | Pattern | Lifespan | Final population | Census |
|---|---|---|---|---|
| Traffic light via T-tetromino | 9 | 12 | 4 blinkers | |
| Phi spark | 17 | 0 | ||
| Interchange | 17 | 18 | 6 blinkers | |
| Two loaves | 12 | 14 | 2 loaves | |
| Two loaves | 12 | 14 | 2 loaves | |
| 2G TL+G | 34 | 17 | 4 blinkers 1 glider | |
| Unnamed spark | 19 | 0 | ||
| Traffic light via longer sequence | 27 | 12 | 4 blinkers | |
| Traffic light via longer sequence | 28 | 12 | 4 blinkers | |
| Fleet | 13 | 24 | 2 ship-ties | |
| Angel predecessor | 14 | 3 | 1 blinker | |
| Tub predecessor | 13 | 4 | 1 tub | |
| Tub predecessor | 14 | 4 | 1 tub | |
| Line-of-six spark | 15 | 0 | ||
| Bakery | 8 | 28 | 2 half-bakeries |
See also
Notes
- ↑ Lifespan is measured from its canonical initial form, not from the form in the generated list.
- ↑ Another honey farm predecessor is listed separately with 7167 occurrences. If included, the total would be 624900.
- ↑ A predecessor of a first cousin of the century is listed separately with 6060 occurrences. If included, the total would be 272064.
- ↑ A Herschel and a block with the same relative position as from a B-heptomino are listed separately with 121316 occurrences. If included, the total would be 366300, which would put the B-heptomino in 5th place. In addition, a predecessor of a B-heptaplet (which is included in the B section in the RLE of two-glider collisions) is listed separately with 11287 occurrences. If also included, the total would be 377587 occurrences.
- ↑ Another predecessor is listed separately later in this list with 12200 occurrences. If included, the total would be 41473, putting it in 14th place. In addition, the object with 16361 occurrences creates a temporary one before quickly crashing into a beehive.
- ↑ A descendant is listed separately with 7533 occurrences. If included, the total would be 29462, which would put the Herschel in 16th place.
- ↑ A descendant is listed separately with 14689 occurrences. If included, the total would be 33196, which would put the Octomino II in 16th place.
- ↑ This pattern is more common without the blinker, but such pattern doesn't get large enough to qualify for the list.
- ↑ This can be turned into a glider almost immediately by placing a tub that interacts with the line of three in generation 2.
- ↑ This pi + block is much more common than other pi + block combinations, but since it has several common predecessors, a single ancestor can't be chosen.
- ↑ Most E-heptominoes don't form this way. In fact, the E-heptomino should be ranked much higher and is ranked 15th in the octo3obj database. In census.rle, there is another not-as-common cousin ranked #82 and a late-generation after-convergence entry ranked #141. Combining #53, #82, and #140 in census.rle gives 19,990 occurrences, ranking it 24th.
- ↑ This number includes all honey farm + block formations with this offset, regardless of what its predecessor was.
- ↑ Another pulsar predecessor is listed separately with 5420 occurrences. If combined, the total would be 12780, which would put the pulsar in 46th place. However, the frequency of the pulsar overall may be overstated, as the soups used to make this list were 8 × 8, and pulsars are more frequent in smaller soups.
References
- ↑ simeks (December 28, 2016). Census of small evolving patterns (discussion thread) at the ConwayLife.com forums
- ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 4.
- ↑ MathAndCode (November 1, 2020). Small predecessors of common objects and evolutionary sequences (discussion thread) at the ConwayLife.com forums
- ↑ MathAndCode (May 4, 2021). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
- ↑ David Raucci (July 2, 2021). Re: Thread For Your Naming Proposals of Unnamed Patterns (discussion thread) at the ConwayLife.com forums
- ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 10.