# Elementary Cellular Automaton Dynamics as Wavelets

Elementary Cellular Automaton Dynamics as Wavelets

Mathematical tools from signal processing can be used to study cellular automata (CA). This Demonstration shows an example of plotting CA dynamics as a wavelet. The CA dynamics consist of the sum of black cells along each row, which represents time. The wavelet is constructed by a process of scaling and translating a signal and separating different frequency components; the graphical representation of the signal highlights the oscillatory behavior (frequency over time). It is possible to observe the four classes of CA behavior as the CA's wavelet form, more complex classes such as III and IV are noisy and harder to distinguish between one another, and classes I and II are simpler.

Class I tends to involve as a set of white or black cells, dying out.

Class II tends to be periodic.

Class III is random.

Class IV comes up with local random structures.