Differential Equations for Creating Complex Cellular Automaton Patterns
Wataru Kunishima, Akinobu Nishiyama, Hiroshi L. TANAKA, Tetsuji Tokihiro · Journal of the Physical Society of Japan · 2004
We propose a method of constructing differential equations directly from cellular automata. Any elementary cellular automata (ECAs) introduced by Wolfram can be transformed into a partial differential equation (PDE) which preserves the time evolution patterns of the ECAs. In particular, some PDEs constructed by the method reproduce complex fractal and self-organizing patterns found in their corresponding ECAs. It is expected that the method can be extended for general cellular automata with more complex rules and/or in higher dimensions.