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Elementary cellular automata show different systems and fractals like rule 30, rule 90, and rule 110. I want to know if there is another classification or type which shows similar structures just like in elementary cellular automata (ECA).

For example what other systems can show structures similar to Sierpinski triangle (which is the same as rule 90 in ECA)?

Is there a method to build rule 30 or 60 using other system than ECA?

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    $\begingroup$ Please define your terms here, I don't understand a word of the above. $\endgroup$
    – vonbrand
    Commented Oct 14, 2015 at 14:34
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    $\begingroup$ Can you please define exactly what you mean by "structures" and by "similar"? What exactly do you mean by "build rule 30 or 60 using other system than ECA?" Right now this seems super-vague. Also, what research have you done? We expect you to do a significant amount of research before asking and to show us in the question what you've done. See cs.stackexchange.com/help/how-to-ask $\endgroup$
    – D.W. ♦
    Commented Oct 14, 2015 at 18:41

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You might take a look at Lindenmayer Systems.

From Wikipedia:

An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial "axiom" string from which to begin construction, and a mechanism for translating the generated strings into geometric structures.

L-systems can be used to generate a Sierpinski triangle.

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    $\begingroup$ Related: Images from context free grammars contextfreeart.org $\endgroup$
    – adrianN
    Commented Jul 28, 2016 at 14:05

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