I have been trying to work on the art/science of developing interesting NNN patterns. It seems difficult to create a rule for most patterns that would quickly come to the imagination, since a bit can only be influence by the five bits directly around and preceding it. So, for example, a rule component that might produce a desirable behavior on the fourth line of a pattern, might conflict with desired behavior on the second line.
One approach I have is to figure out the rule for a very basic two or three line pattern, starting with a single pixel. E.g., rule 0,4,1,2 gives us:
O O O O X O O O O
O O X O O X O O O
X O O O X O X O O
The overall graphic is not very interesting, though it is a bit more so as you zoom into the pattern which walks to one side:
Also when it collides with itself and bends:
But, how can we make this design more interesting? Next step is to try to introduce a rule component to try to prevent convergence, i.e., disrupt it when it starts to get boring. One interesting tweak was 0,6,1,2 (X O O O X -> X) creating a triangle texture:
Another was 0,20,1,2 (X O X O O -> X), which does not prevent convergence, but it does create a scale-like texture:
The Libre Hacker 