Above you can see a 1D cellular automaton using probabilities to determine life and death of cells. Choose the probabilities p1,p2 and p3 (in percents) and see some nice patterns arose.
Moreover you can find this random 1d cellular automaton in my fab tool.
Here's the principle: We compute one line after another,
and to know the new living/dead state of a cell, we check
the previous state of it and both its neighbours. Let's mark
* a living cell and . a dead
one. Then we have 8 possibilities (with a lot so symmetries though) according to neighbours:
*** : center cell will live with probability p1
*.* : center cell will live with probability p2
**. : center cell will live with probability p3
.** : center cell will live with probability p3
..* : center cell will live with probability 1-p3
*.. : center cell will live with probability 1-p3
.*. : center cell will live with probability 1-p2
... : center cell will live with probability 1-p1
Some values to try for(p1;p2;p3):
(90;70;60) which is default
(95;10;90) vertical raindrops
(100;70;35) kind of triangles appearing
(0;100;100) funny and small arches but no need for randomness here ;)
(100;0;0) another non random 1D cellular automaton