
https://www.worldscientific.com/worldscibooks/10.1142/4702#t...
It's an amazing book even if it is a couple of decades old now.
Stephen Wolfram's, "A New Kind of Science" is also good. He has been studying and writing about CAs since the 80s.
CAs are used for many things. I am just starting to look at Ilachinski's work on combat simulation.
There was a paper comparing PDEs to CAs a while ago. I'll look up the link.
There are also some articles from Wolfram that make good introductions. Mostly those from the old days in which "I" wouldn't be the subject of every second of his sentences. In particular:
Universality and Complexity in Cellular Automata Physica D: Nonlinear Phenomena 10, no. 1–2 (1984): 1–35
Computation Theory of Cellular Automata Communications in Mathematical Physics 96, no. 1 (1984): 15–57