One option is a 'totalistic' CA which looks at the average value of a given neighborhood, and can have more than two states.
http://mathworld.wolfram.com/TotalisticCellularAutomaton.htm...
Or you could generate CAs with different starting conditions. Some beautiful elementary CAs don't 'show up' with just one initial point.
It's a "Robust First" asynchronous distributed fault tolerant cellular-automata-like computer architecture.
Robust programs running on massively parallel unreliable hardware can actually tolerate hardware failure and repair themselves. The Demon Hoard Sort algorithm is an inherently robust sorting algorithm for the Moveable Feast Machine.
http://movablefeastmachine.org/
The "Distributed City Generation" video demonstrates a Movable Feast Machine rule that builds a self-healing city that fills all available space with urban sprawl, with cars that drive between buildings, and city streets that adaptively learn how to route the cars to their nearest destinations, and the city even repairs itself after disasters!
https://www.youtube.com/watch?v=XkSXERxucPc
Here's some more info: