Langton's ant
a two-dimensional universal Turing machine with a very simple set of rules but complex emergent behavior.
Rules:
LR
LRL
LRR
LLRR
LRLRR
RRLLRL
RLRLRLRL
LRRRRRLLR
RRLLLRLLLRRR
LLRRRLRLRLLR
LRRRLLRLLRRRRLRRLRLRLRLLRRLRR
Steps at once:
1
10
100
1000
10000
100000
1000000
Dimension:
200
500
1000
1500
2000
3000
Fade:
yes
no