This is a collection of images created by the programs in Xtoys. The above pictures are for the classic life cellular automaton. Newborn cells are red, older ones blue, just expired green, and a light grey background indicates where there has been activity in the recent past. The second picture shows the spoils after a shootout between five glider guns.
Trees grow randomly while fire fronts burn them down. Note the appearance of large scale phenomena from a local dynamics.
The above uses N,NE,W,SW,S, and SE neighbors, and has births for 2, 5, or 6 live neighbors and survivors for 4 or 5 live neighbors. This rule has lots of different glider species.
This involves the eight cell neighborhood, births on any but zero neighbors, and survivors in all cases, but then the rule is modified by xoring this result with the state one step back in time. This is a reversible rule.
Fredkin's modulo 2 rule, where each cell is xored with all of its neighbors. Any initial picture is replicated a number of times given by the number of active neighbors (here 4). The second image is from the same rule starting with a single set pixel.
To mimic a hexagonal lattice, use N,NE,E,S,SW, and W neighbors. This is the mod 2 rule after starting from a single set site.
Births on 2 neighbors and never any survivors with the eight cell neighborhood. The empty state is a rather unstable situation, although simple gliders are supported.
Counting only top neighbors allows one to study some simple one dimensional automata where the vertical direction represents time.
The progress of an avalanch in the Bak, Tang, Wiesenfeld sandpile model. Note that the final avalanche region is simply connected.
The Dhar burning algorithm in progress on the initial state of the above series. Every cell will eventually tumble exactly once.
The identity sandpile state on a 198 by 198 lattice.
On a periodic lattice an avalanch can go on forever. Here is a state during one of these "Escher" cascades.
The two dimensional Ising model on a 190 by 190 lattice at a temperature near the critical value.
Nucleation in the two dimensional Ising model at a low temperature just after a flip in the sign of an applied magnetic field.
The 16 state Potts model at an energy density constrained to be in the gap between the ordered and disordered phases.