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) |
128 | 121316 | 0.196 | |
| Teardrop | 20 | 64485 | 0.104 | |
| I-heptomino | 247 | 53177 | 0.086 | |
| Two-glider octomino | 385 | 50178 | 0.081 | |
| Long bun (object hassled in Jason's p33) | 53 | 48239 | 0.078 | |
| Procrastinator [2][3] | 73 | 46879 | 0.076 | |
| Blonk-tie | 552 | 38554 | 0.062 | |
| Unnamed (active region from the beginning of Iwona) |
238 | 37747 | 0.061 | |
| U-turner[4] | 163 | 29273[note 5] | 0.047 | |
| Herschel descendant hassled in period-184 glider gun, H' (without its first natural glider) |
106 | 29196 | 0.047 | |
| R-turner (name unofficial[5]) | 268 | 28314 | 0.046 | |
| Original diehard | 130 | 27077 | 0.044 | |
| Object hassled in Jason's p22 | 65 | 25303 | 0.041 | |
| Traffic light hitting block (creating block and blinker) |
47 | 24725 | 0.040 | |
| Dove | 200 | 23603 | 0.038 | |
| Unnamed (soon evolves into a pi and loaf) (evolves from o3bo$ob3o$6bo) |
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 hitting block, leaving single beehive | 69 | 17795 | 0.0289 | |
| Traffic light hitting block, leaving two blinkers | 36 | 17656 | 0.0286 | |
| Object hassled in Karel's p177 | 153 | 17620 | 0.0285 | |
| Unnamed, dies out | 18 | 17007 | 0.0275 | |
| Object hassled in Merzenich's p64 | 34 | 16764 | 0.0271 | |
| Unnamed, evolves to 7 blinkers | 35 | 16695 | 0.0270 | |
| Traffic light hitting block | 173 | 16414 | 0.0266 | |
| A single unit in the 3c/7 wave, dies out (evolves into U-turner descendent and a beehive) |
27 | 16361 | 0.0265 | |
| Traffic light hitting block | 211 | 15854 | 0.0257 | |
| Clean bi-block predecessor | 44 | 15621 | 0.0253 | |
| Traffic light hitting block | 22 | 15505 | 0.0251 | |
| Lumps of muck hitting block | 68 | 15475 | 0.0251 | |
| Intermediate generation of octomino II | 94 | 14689 | 0.0251 | |
| Unnamed six-cell pattern listed as 5.s.1[6] | 49 | 14585 | 0.0236 | |
| Unnamed beehive edge-shooter[note 8] | 61 | 14525 | 0.0235 | |
| Unnamed, dies out | 49 | 14509 | 0.0235 | |
| Unnamed | 17 | 13997 | 0.0227 | |
| Unnamed methuselah making procrastinator and beehive |
1675 | 13661 | 0.0221 | |
| Active region in cis-beacon on anvil predecessor | (click above to open LifeViewer) |
320 | 13484 | 0.0218 |
| Unnamed; pi-heptomino hitting boat | (click above to open LifeViewer) |
130 | 12411 | 0.0201 |
| U-turner 30-generation predecessor | (click above to open LifeViewer) |
193 | 12200 | 0.0197 |
Of the top 96, the E-heptomino ranks 53rd with 11035 occurences,[note 9] the queen bee ranks 81st (7910 occurrences), and the pulsar ranks 86th (7360 occurrences).[note 10] 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.
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 |
|---|---|---|
| Traffic light via T-tetromino | 9 | |
| Phi spark | (click above to open LifeViewer) |
17 |
| Interchange | (click above to open LifeViewer) |
17 |
| Two loaves | (click above to open LifeViewer) |
12 |
| Two loaves | (click above to open LifeViewer) |
12 |
| 2G TL+G | (click above to open LifeViewer) |
34 |
| Unnamed spark | (click above to open LifeViewer) |
17 |
| Traffic light via longer sequence | (click above to open LifeViewer) |
27 |
| Traffic light via longer sequence | (click above to open LifeViewer) |
28 |
| Fleet | (click above to open LifeViewer) |
13 |
| Angel predecessor | (click above to open LifeViewer) |
14 |
| Tub predecessor | (click above to open LifeViewer) |
14 |
| Table | (click above to open LifeViewer) |
15 |
| Bakery | (click above to open LifeViewer) |
8 |
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.
- ↑ 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. 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.