Abstract
Cellular automata (CAs) have been successfully used to investigate complex phenomena across a broad range of research fields. Standard CAs can be extended by applying a novel algorithm known as the recursive estimation of neighbors. This process allows the construction of non-uniform CAs that are composed of cells with different perception areas parameterized by an extra radius. This paper proposes a non-uniform CA called Fractal CA (F-CA), which is composed of cells with self-similar fractal arrangement. By focusing on the extension of 1D elementary CAs, certain characteristics of standard CAs are carried over into F-CAs, including time reversibility of the linear rules. F-CAs based on 2D outer-totalistic CAs are also mentioned briefly.
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