So i know that rule 110 from Elementary Cellular Automata is universal but i am wondering if we had other chaotic behaviors let's say there exists a system that shows nearly infinite chaotic behaviors {a structure at a time} similar to ECA structures, how can we prove or disprove universality from that system ?Suppose we have a system with one specific rule to execute and the input can be defined by different number of cells {i.e input = 5 cells} these 5 cells for example can show (2000) chaotic behavior... 4 cells can show nearly (1800), for example to get a structure from the (1800) structures, i can change the 4 cells by changing the rule set of these 4 cells just like in ECA => 'two white cells will result in a black cell', i can define a similar rule set on the 4 cells, 5 cells or more generally on x cells where x < infinite. That system with same input {4 cells} with different rule set can simulate most of the structures in Elementary Cellular Automata like rule 30, 90 & 60 and others, what can be proved about such system and how universality is related to it ?
What is the relation between universality and chaotic behavior in Elementary Cellular Automata?
complexity theory;computability;cellular automata