Transition phenomena in cellular automata rule space by Li, W., Packard, N. H., & Langton, C. G. (1990)

Cellular automata
(Li, Packard, and Langton 1990)


This foundational paper follows Langton’s work on chaos and the lambda parameter. It uses information-theoretic measures to try and understand the structure of the space of CA rules. The authors come up with a classification in 6 classes:

  1. Spatially homogeneous fixed points
  2. Spatially inhomogeneous fixed points
  3. Periodic behavior
  4. Locally chaotic behavior
  5. Chaotic behavior
  6. Complex behavior

Wolfram’s class I is equivalent to class 1, class II is equivalent to class 2, 3 and 4. Class III and IV are the same as class 5 and 6.


This literature seems relevant to cellular automata classification. I’m still not sure about this and will need to think about it. This is certainly one of the first examples of work on these questions.


Li, Wentian, Norman H. Packard, and Chris G. Langton. 1990. “Transition Phenomena in Cellular Automata Rule Space.” Physica D: Nonlinear Phenomena 45 (1):77–94.

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