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[note 1] | Occurrences | Relative frequency |
|---|---|---|---|---|
| Honey farm predecessor (bun shown) | 17 | 617733[note 2] | 1.000 | |
| R-pentomino | 1103 | 531779 | 0.861 | |
| Pi-heptomino | 173 | 471544 | 0.763 | |
| Lumps of muck | 63 | 310237 | 0.502 | |
| Century | 103 | 266004[note 3] | 0.430 | |
| B-heptomino | 148 | 244984[note 4] | 0.397 | |
| Wing | 104 | 133659 | 0.216 | |
| Herschel with block (B-heptomino descendant) | (click above to open LifeViewer) |
128 | 121316 | 0.196 |
| Teardrop | 20 | 64485 | 0.104 | |
| I-heptomino | 247 | 53177 | 0.086 | |
| Two-glider octomino | 385 | 50178 | 0.081 | |
| Object hassled in Jason's p33 (generates a bi-block and another block) | (click above to open LifeViewer) |
53 | 48239 | 0.078 |
| Procrestinator [2][3] | (click above to open LifeViewer) |
73 | 46879 | 0.076 |
| Blonk-tie | 552 | 38554 | 0.062 | |
| Unnamed (active region from the beginning of Iwona) | (click above to open LifeViewer) |
238 | 37747 | 0.061 |
| U-turner[4] | 163 | 29273[note 5] | 0.047 | |
| Object hassled in period-184 glider gun, H' (Herschel without its first natural glider) | (click above to open LifeViewer) |
106 | 29196 | 0.047 |
| R-turner (name unofficial[5]) | (click above to open LifeViewer) |
268 | 28314 | 0.046 |
| Original diehard | 130 | 27077 | 0.044 | |
| Object hassled in Jason's p22 | (click above to open LifeViewer) |
65 | 25303 | 0.041 |
| Traffic light hits block (creating block and blinker) | (click above to open LifeViewer) |
47 | 24725 | 0.040 |
| Dove | 200 | 23603 | 0.038 | |
| Unnamed (soon evolves into a pi and loaf) (evolves from o3bo$ob3o$6bo) | (click above to open LifeViewer) |
346 | 22654 | 0.0367 |
| Herschel (by itself) | 128 | 21929[note 6] | 0.0355 | |
| Butterfly | 33 | 18593 | 0.0301 | |
| Octomino II | 116 | 18507[note 7] | 0.0300 | |
| Traffic light hits block, leaving single beehive | (click above to open LifeViewer) |
69 | 17795 | 0.0289 |
| Traffic light hits block, leaving two blinkers | (click above to open LifeViewer) |
36 | 17656 | 0.0286 |
| Object hassled in Karel's p177 | (click above to open LifeViewer) |
153 | 17620 | 0.0285 |
| Unnamed, dies out | (click above to open LifeViewer) |
18 | 17007 | 0.0275 |
| Object hassled in Merzenich's p64 | (click above to open LifeViewer) |
34 | 16764 | 0.0271 |
| Unnamed | (click above to open LifeViewer) |
35 | 16695 | 0.0270 |
| Traffic light hits block | (click above to open LifeViewer) |
173 | 16414 | 0.0266 |
| Unnamed, dies out (evolves into U-turner decendent and a beehive.) | (click above to open LifeViewer) |
27 | 16361 | 0.0265 |
| Traffic light hits block | (click above to open LifeViewer) |
211 | 15854 | 0.0257 |
| Clean bi-block predecessor | (click above to open LifeViewer) |
44 | 15621 | 0.0253 |
| Traffic light hits block | (click above to open LifeViewer) |
22 | 15505 | 0.0251 |
| Lumps of muck hits block | (click above to open LifeViewer) |
68 | 15475 | 0.0251 |
| Intermediate generation of octomino II | (click above to open LifeViewer) |
94 | 14689 | 0.0251 |
| Unnamed six-cell pattern[note 8] | (click above to open LifeViewer) |
49 | 14585 | 0.0236 |
| Unnamed[note 9] | (click above to open LifeViewer) |
61 | 14525 | 0.0235 |
| Unnamed | (click above to open LifeViewer) |
49 | 14509 | 0.0235 |
| Unnamed | (click above to open LifeViewer) |
17 | 13997 | 0.0227 |
| Unnamed methuselah | (click above to open LifeViewer) |
1675 | 13661 | 0.0221 |
Of the top 96, the E-heptomino ranks 53rd with 11035 occurences,[note 10] the queen bee ranks 81st (7910 occurrences), and the pulsar ranks 86th (7360 occurrences).[note 11] The F-heptomino (5154 occurences), thunderbird (6161 occurences), 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), a clean paperclip (1053), gliders by the dozen (855), and a clean bipond (830).
This census for small, common active regions may provide insights into finding bottlenecks for new conduits.
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 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.
- ↑ See Lifeline Volume 4
- ↑ This pattern is more common without the blinker, but such pattern doesn't get large enough to qualify for the list.
- ↑ Another active region that converges to the E-sequence is listed separately with 7884 occurrences. If combined, the total would be 18919, which would put the E-sequence in 25th place.
- ↑ Another pulsar predecessor is listed separately with 5420 occurrences. If combined, the total would be 12780, which would put the pulsar in 46th place.
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