  This study focuses on an extended model of a standard cellular automaton (CA)
that includes an extra index consisting of a radius that defines a perception
area for each cell in addition to the radius defined by the CA rule. Extended
standard CA rules form a sequence ordered by this index, which includes the CA
rule as its first term. This extension aims at constructing a model that can be
used within the CA framework to study the relationship between information
processing and pattern formation in collective systems. Although the extension
presented here is merely an extrapolation to a CA with a larger rule
neighborhood, the extra radius can be interpreted as an individual difference
of each cell, which provides a new perspective to CA. Some pattern formations
in extended one-dimensional elementary CAs and two-dimensional Life-like CAs
are presented. It is expected that the extended CA can be applied to various
simulations of complex systems and other fields.
