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Cellular Automata as defined by wolfram alpha:
"A cellular automaton is a collection of "colored" cells on a grid of specified shape that evolves through a number of discrete time steps according to a set of rules based on the states of neighboring cells."
If you are familiar with Conways Game of life, Cellular automata is like a more advanced version where you can change the ruleset. It seems to operate similar to pascals triangle where the top row influences the next.
Ill be honest with you, i dont really know that much about cellular automata. Its abit too mathy for me. So do your own research if you want to know more. What i do know, however, is that a couple of these rule sets generate sierpinskis triangle. these rulesets are
Speaking of Conways Game of Life, you can also arrange the cells in a way to generate the S-Triangle.