Measuring complexity created by cellular automata is a vast subject.
In (Wuensche 1999), the author uses the entropy of rule table lookup frequencies to evaluate the complexity of a CA.
- Wuensche, Andrew. 1999. "Classifying Cellular Automata Automatically: Finding Gliders, Filtering, and Relating Space-Time Patterns, Attractor Basins, and the Z Parameter". Complexity 4 (3):47–66. DOI.