We have an interesting evolution rule with complex behavior by an ample set of localizations (gliders, spaceships, oscillators, glider guns and puffer trains). Our evolution rule is called "Diffusion Rule" (rediscovered April 2005).
Similar to The Game of Life our evolution rule have complex behavior and also reaction diffusion behavior. At the moment, we found several useful objects to think about the logical universality of Diffusion Rule like: gliders, glider guns, puffers train, blinkers and eaters. Several collisions like: reflections (FANOUT gate), multiplications, annihilations, delays and reactions of diffusion type (powered by Golly system).
Diffusion Rule evolves in two-dimension, two states with Moore neighborhood. Several Diffusion Rule objects and reactions are found: different types of gliders, puffer trains, and glider guns.
Also, you can read our paper "Localization dynamic in a binary two-dimensional cellular automaton: the Diffusion Rule" [PDF].
- majority-gate.rle - Collisions of gliders simulating a semi-majority logical gate in Diffusion Rule.
- FANOUT-halt.rle - Multiple reflections and annihilations between gliders and oscillators (FANOUT gate).
Also, you can download or see two movies illustrating a new glider gun [newGun.mov] in Diffusion Rule (October 21, 2006) and a good example of synchronization (like luminescence process) in Diffusion Rule with thousands of cells [luminescence.mov].
In figure 1 we show three gliders hitting, later of collisions traveling to left produce a puffer train generating two cycle life of period four. Diffusion process is growing symmetrically in both cartesian planes.
Fig. 1 Initial condition with three glidres (triple collision after of 150 generations).