OCA:DryLife

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DryLife
x=0, y = 0, rule = B37/S23 ! #C [[ THEME Inverse ]] #C [[ RANDOMIZE2 THUMBLAUNCH OFF THUMBNAIL THUMBSIZE 2 GRID ZOOM 4 WIDTH 500 HEIGHT 500 LABEL 90 -20 2 "#G" AUTOSTART PAUSE 2 GPS 8 LOOP 256 ]]
LifeViewer-generated soup (refreshes with page)
Rulestring 23/37
B37/S23
Rule integer 6280
Character Explosive
Black/white reversal B0123478/S0234678

DryLife is a Life-like cellular automaton in which cells survive from one generation to the next if they have 2 or 3 neighbours, and are born if they have 3 or 7 neighbours. The rule behaves in an explosive manner, as small patterns, such as the stairstep hexomino, may exhibit chaotic growth.

Patterns

DryLife is so named because the standard spaceships from normal life; lightweight spaceship, middleweight spaceship, and heavyweight spaceship — also known as "fishes" — do not work, though the glider does. Some other spaceships, such as the x66, weekender and loafer, work in this rule. The copperhead evolves into the closely related c/10 goldenhead, differing from copperhead by two cells in one phase, and it supports the pseudo-tagalong in fireship as well.

A pair of correctly spaced B-heptominoes (as in the twin bees shuttle) evolves into a messy period-160 c/2 orthogonal puffer.

x = 19, y = 15, rule = B37/S23 4b2o$b2obo9bo$o$o12bo$3o8bob3o$12bo3bo5$4b3o6bo$4bo11bo$4bo$5b2obo6bob 2o$8b2o5bobo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]] #C [[ ZOOM 16 HEIGHT 350 AUTOSTART GPS 7 TRACKLOOP 28 -9/28 0 ]]
A 2-engine 9c/28 spaceship found by Paul Tooke
(click above to open LifeViewer)
RLE: here Plaintext: here
Catagoluehere

A new speed allowed by DryLife is 9c/28 orthogonal. Technology travelling at this speed relies on the R-pentomino. Two R-pentominoes constitute a small symmetric 9c/28 orthogonal pond puffer, or a spaceship. A 3-glider collision that synthesises a R-pentomino via beehive works well, so guns and breeders have been constructed that fire spaceships and rakes of this speed respectively.

As for oscillators, there is a small period-32 reflectorless rotating oscillator called spinner, which gives banana sparks and is therefore capable of reflecting gliders by 90 degrees. Jason Summers found that a collision between a glider and a half-open twirling T-tetsons 2 produces two 90-degree gliders while sustaining the pre-pulsar engine, resulting in a period-60 glider gun; a blocker and a spinner can be added as filters for a p480 gun.

x = 21, y = 13, rule = B37/S23 8bo3bo$7bobobobo$8b2ob2o$b2o15b2o$o2bo13bo2bo$b3o13b3o2$b3o13b3o$o2bo 13bo2bo$b2o15b2o$8b2ob2o$7bobobobo$8bo3bo! #C [[ THUMBSIZE 2 THEME 6 GRID GRIDMAJOR 0 SUPPRESS THUMBLAUNCH ]]
The flower garden (click above to open LifeViewer)
RLE: here Plaintext: here

The "flower garden", a common constellation composed of two bi-boats and two cis-mirrored buns which evolves from some honey farm predecessors like bun, is shown to the right.

Universality

There is a proof sketch of DryLife's universality on ConwayLife.com forums. It is a proof-scheme covering all rules in the outer-totalistic rulespace between B3/S23 and B3678/S23678.[1]

In 2018, Peter Naszvadi constructed an explicit Rule 110 unit cell in DryLife, proving its Turing-completeness.[2] The pattern itself is basically a meta-polyglot, covering some related cellular automata in which the pattern only differs in some parts (in this case, the guns).

References

  1. Peter Naszvadi (December 12, 2016). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums
  2. Peter Naszvadi (March 29, 2018). Re: List of the Turing-complete totalistic life-like CA (discussion thread) at the ConwayLife.com forums

External links