Is there a similar categorization to Elementary Cellular Automata? 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?
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.