List of common evolutionary sequences: Difference between revisions

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! Sequence  !! Pattern !! Lifespan{{refn|group=note|Lifespan is measured from its canonical initial form, not from the form in the generated list.}} !! Occurrences !! Relative frequency
! Sequence  !! Pattern !! Lifespan{{refn|group=note|Lifespan is measured from its canonical initial form, not from the form in the generated list.}} !! Occurrences !! Relative frequency
|-
|-
| [[Honey farm]] predecessor ||{{EmbedViewer|rle = 2o$obo$obo$bo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 17 || 617733 || 1.000
| [[Honey farm]] predecessor ([[bun]] shown]] ||{{EmbedViewer|rle = 2o$obo$obo$bo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 17 || 617733{{refn|group=note|Another honey farm predecessor is listed separately with 7167 occurrences. If included, the total would be 624900.}} || 1.000
|-
|-
| [[R-pentomino]] ||{{EmbedViewer|pname = rpentomino|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 1103 || 531779 || 0.861
| [[R-pentomino]] ||{{EmbedViewer|pname = rpentomino|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 1103 || 531779 || 0.861
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| [[Lumps of muck]] ||{{EmbedViewer|pname = stairstephexomino|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 63 || 471544 || 0.502
| [[Lumps of muck]] ||{{EmbedViewer|pname = stairstephexomino|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 63 || 471544 || 0.502
|-
|-
| [[Century]] ||{{EmbedViewer|pname = century|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 103 || 266004 || 0.430
| [[Century]] ||{{EmbedViewer|pname = century|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 103 || 266004{{refn|group=note|A predecessor of a first cousin of the century is listed separately with 6060 occurrences. If included, the total would be 272064.}} || 0.430
|-
|-
| [[B-heptomino]] ||{{EmbedViewer|pname = bheptomino|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 148 || 244984 || 0.397
| [[B-heptomino]] ||{{EmbedViewer|pname = bheptomino|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 148 || 244984{{refn|group=note|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.}} || 0.397
|-
|-
| [[Wing]] ||{{EmbedViewer|pname = wing|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 104 || 133659 || 0.216
| [[Wing]] ||{{EmbedViewer|pname = wing|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 104 || 133659 || 0.216
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| [[Blonk-tie]] ||{{EmbedViewer|pname = blonktie|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 552 || 38554 || 0.062
| [[Blonk-tie]] ||{{EmbedViewer|pname = blonktie|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 552 || 38554 || 0.062
|-
|-
| Unnamed ||{{EmbedViewer|rle = ob3o$2o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 238 || 37747 || 0.061
| Unnamed (active region from the beginning of [[Iwona]]) ||{{EmbedViewer|rle = ob3o$2o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 238 || 37747 || 0.061
|-
|-
| U-turner (name unofficial<ref name="post129564" />) ||{{EmbedViewer|rle = b3o$b3o$obo$2o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 163 || 29273 || 0.047
| U-turner (name unofficial<ref name="post129564" />) ||{{EmbedViewer|rle = b3o$b3o$obo$2o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 163 || 29273 || 0.047
|-
|-
| Object hassled in [[period-184 glider gun]], H' ||{{EmbedViewer|rle = 2o$o2b2o$bo2bo$b3o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 106 || 29196 || 0.047
| Object hassled in [[period-184 glider gun]], H' (Herschel without its [[first natural glider]]) ||{{EmbedViewer|rle = 2o$o2b2o$bo2bo$b3o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 106 || 29196 || 0.047
|-
|-
| Unnamed ||{{EmbedViewer|rle = 2b2o$4bo$o2bo$3o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 268 || 47154 || 0.046
| Unnamed ||{{EmbedViewer|rle = 2b2o$4bo$o2bo$3o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 268 || 47154 || 0.046
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| Object hassled in [[Jason's p22]] ||{{EmbedViewer|rle = 2b3o$bo3bo$o4bo$bob2o$2bo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 65 || 25303 || 0.041
| Object hassled in [[Jason's p22]] ||{{EmbedViewer|rle = 2b3o$bo3bo$o4bo$bob2o$2bo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 65 || 25303 || 0.041
|-
|-
| Traffic light hits block ||{{EmbedViewer|rle = 2o$2o4bo$5b3o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 47 || 24725 || 0.040
| Traffic light hits block (creating block and blinker) ||{{EmbedViewer|rle = 2o$2o4bo$5b3o!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 47 || 24725 || 0.040
|-
|-
| [[Dove]] ||{{EmbedViewer|pname = dove|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 200 || 23603 || 0.038
| [[Dove]] ||{{EmbedViewer|pname = dove|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 200 || 23603 || 0.038
|-
|-
| Unnamed ||{{EmbedViewer|rle = o2bo$bob2o$bo3b2o$4bo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 47 || 22654 || 0.0367
| Unnamed (soon evolves into a pi and loaf) ||{{EmbedViewer|rle = o2bo$bob2o$bo3b2o$4bo!|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 47 || 22654 || 0.0367
|-
|-
| [[Herschel]] (by itself) ||{{EmbedViewer|pname = herschel|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 128 || 21929 || 0.0355
| [[Herschel]] (by itself) ||{{EmbedViewer|pname = herschel|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 128 || 21929{{refn|group=note|A descendant is listed separately with 7533 occurrences. If included, the total would be 29462, which would put the Herschel in 16th place.}} || 0.0355
|-
|-
| [[Butterfly]] ||{{EmbedViewer|pname = butterfly|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 33 || 18593 || 0.0301
| [[Butterfly]] ||{{EmbedViewer|pname = butterfly|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 33 || 18593 || 0.0301
|-
|-
| [[Octomino II]] ||{{EmbedViewer|pname = octominoii|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 116 || 18507 || 0.0300
| [[Octomino II]] ||{{EmbedViewer|pname = octominoii|viewerconfig = #C [[ THUMBSIZE 4 ]]}}|| 116 || 18507{{refn|group=note|A descendant is listed separately with 14689 occurrences. If included, the total would be 33196, which would put the Octomino II in 16th place.}} || 0.0300
|}
|}


Of the top 96, the [[E-heptomino]] ranks 53rd, the [[queen bee]] ranks 81st, and the [[pulsar]] ranks 86th. The [[F-heptomino]], [[thunderbird]], and [[switch engine]] do not make the top 96. The [[Z-hexomino]] ranks 146th.
Of the top 96, the [[E-heptomino]] ranks 53rd with 11035 occurences,{{refn|group=note|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.}} the [[queen bee]] ranks 81st (7910 occurrences), and the [[pulsar]] ranks 86th (7360 occurrences).{{refn|group=note|Another pulsar predecessor is listed separately with 5420 occurrences. If combined, the total would be 12780, which would put the pulsar in 46th place.}} 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).


This census for small, common active regions may provide insights into finding bottlenecks for new [[conduit]]s.
This census for small, common active regions may provide insights into finding bottlenecks for new [[conduit]]s.

Revision as of 19:00, 25 May 2021

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]]
2o$obo$obo$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 17 617733[note 2] 1.000
R-pentomino
x = 3, y = 3, rule = B3/S23 b2o$2o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 1103 531779 0.861
Pi-heptomino
x = 3, y = 3, rule = B3/S23 3o$obo$obo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 173 471544 0.763
Lumps of muck
x = 4, y = 3, rule = B3/S23 2o$b2o$2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 63 471544 0.502
Century
x = 4, y = 3, rule = B3/S23 2b2o$3o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 103 266004[note 3] 0.430
B-heptomino
x = 4, y = 3, rule = B3/S23 ob2o$3o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 148 244984[note 4] 0.397
Wing
x = 4, y = 4, rule = B3/S23 b2o$o2bo$bobo$2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 104 133659 0.216
Herschel with block (B-heptomino descendant)
o11b2o$3o9b2o$obo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 128 121316 0.196
Teardrop
x = 4, y = 4, rule = B3/S23 b3o$o2bo$o2bo$b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 20 64485 0.104
I-heptomino
x = 4, y = 4, rule = B3/S23 2o$bo$b2o$2b2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 247 53177 0.086
Two-glider octomino
x = 4, y = 4, rule = B3/S23 2b2o$2b2o$3o$bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 385 50178 0.081
Generates a bi-block and another block
bobo$o2b2o$o2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 53 48239 0.078
Procrestinator [2][3]
o$3o$3bo$b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 73 46879 0.076
Blonk-tie
x = 3, y = 5, rule = B3/S23 2o$2o$2bo$2bo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 552 38554 0.062
Unnamed (active region from the beginning of Iwona)
ob3o$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 238 37747 0.061
U-turner (name unofficial[4])
b3o$b3o$obo$2o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 163 29273 0.047
Object hassled in period-184 glider gun, H' (Herschel without its first natural glider)
2o$o2b2o$bo2bo$b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 106 29196 0.047
Unnamed
2b2o$4bo$o2bo$3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 268 47154 0.046
Original diehard
x = 8, y = 3, rule = B3/S23 6bo$2o$bo3b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 130 27077 0.044
Object hassled in Jason's p22
2b3o$bo3bo$o4bo$bob2o$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 65 25303 0.041
Traffic light hits block (creating block and blinker)
2o$2o4bo$5b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 47 24725 0.040
Dove
2b2o$bo2bo$o2bo$3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 200 23603 0.038
Unnamed (soon evolves into a pi and loaf)
o2bo$bob2o$bo3b2o$4bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
 47 22654 0.0367
Herschel (by itself)
x = 3, y = 4, rule = B3/S23 o$3o$obo$2bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 128 21929[note 5] 0.0355
Butterfly
x = 4, y = 4, rule = B3/S23 o$2o$obo$b3o! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 33 18593 0.0301
Octomino II
x = 4, y = 4, rule = B3/S23 bo$3o$ob2o$3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ THUMBSIZE 4 ]]
(click above to open LifeViewer)
RLE: here Plaintext: here
 116 18507[note 6] 0.0300

Of the top 96, the E-heptomino ranks 53rd with 11035 occurences,[note 7] the queen bee ranks 81st (7910 occurrences), and the pulsar ranks 86th (7360 occurrences).[note 8] 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).

This census for small, common active regions may provide insights into finding bottlenecks for new conduits.

See also

Notes

  1. ↑ Lifespan is measured from its canonical initial form, not from the form in the generated list.
  2. ↑ Another honey farm predecessor is listed separately with 7167 occurrences. If included, the total would be 624900.
  3. ↑ A predecessor of a first cousin of the century is listed separately with 6060 occurrences. If included, the total would be 272064.
  4. ↑ 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.
  5. ↑ A descendant is listed separately with 7533 occurrences. If included, the total would be 29462, which would put the Herschel in 16th place.
  6. ↑ A descendant is listed separately with 14689 occurrences. If included, the total would be 33196, which would put the Octomino II in 16th place.
  7. ↑ 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.
  8. ↑ 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

  1. ↑ simeks (December 28, 2016). Census of small evolving patterns (discussion thread) at the ConwayLife.com forums
  2. ↑ Robert Wainwright (December 1971). Lifeline, vol 4, page 4.
  3. ↑ MathAndCode (November 1, 2020). Small predecessors of common objects and evolutionary sequences (discussion thread) at the ConwayLife.com forums
  4. ↑ MathAndCode (May 4, 2021). Re: Thread for basic questions (discussion thread) at the ConwayLife.com forums
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