tslil clingman: cellular automata

I have long been fascinated with emergent complexity in systems, and cellular automata have proven to be an excellent playground in which to derive this phenomenon. There's much to be said about this area, though unfortunately not too much (to my knowledge, please let me know!) of it is rigorous just yet.


Below you can find some of my constructions and findings in the rule set B36/S245 which i call ‘ridiculous pond’. Part of what makes this such an interesting rule is the existence of an almost-replicator (in Golly compatible RLE): 6o$o4bo$b4o!

Simulation of the almost-replicator

This pattern seems to exhibit replicator-like behaviour, but it has some curious features: it drops oscillators, it appears reflected some time later, and the collisions with the oscillators result in more copies of it. It is possible to place two copies of the almost-replicator side-by-side (discovered by Mark Niemiec 1994, 6o7b6o$o4bo7bo4bo$b4o9b4o!) to form something closer to a traditional replicator, but the overall behaviour is still nuanced.

Through computer search or hand-engineering we may find many ways to eliminate the oscillators and so contain the almost-replicator and transform it into an oscillator.

Examples of stabilisation

In fact it is possible to combine the almost-replicators in a variety of manners to produce Gosper-esque guns for the commonly occurring c/7 jelly glider.

Two corner-style jelly guns

Using these guns and some glider synthesis it is possible to create more complicated spaceship guns. Below you can find two such patterns i engineered.

The period 408 chevron gun

The above is a relatively straightforward, 8 glider synthesis of a spaceship – though it does make use of fairly tight packing of corner-style jelly guns. Perhaps future technology will eliminate the need for the bounding-box overlap the pattern currently exhibits.

The shuttler gun has an extremely large bounding box (2011x2592) but is ultimately a 10 glider synthesis. The pattern makes use of what amounts to timed ROM units – glider loops with sensing and duplication machinery – and the simplest solution to the constraints of the period of the very slow shuttler 14c/300 spaceship, the c/7 jelly, and some intermediate oscillators and patterns, resulted in the generous proportions and period of the gun. Undoubtedly there is room for improvement, but the existence of such a pattern has been established.

As the links imply, there is prior work on this rule (David Eppstein here and on the online database of gliders), but i believe these glider synthesis are original and affirmatively respond to Eppstein's question of the existence of such glider synthesis guns.

Computer search of this rule has been very fruitful for c/2 (sample rle), c/3 (sample rle), c/4 (sample rle), and c/5 (sample rle) spaceships. An enormous variety of ships have been found, and some are arbitrarily extendable.

A sample collection of spaceships, puffers, still lifes, oscillators, and miscellaneous patterns is available here (rle).

Finally, i am currently investigating other technology in this rule set, including: