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Published in:
2010 | OriginalPaper | Chapter
RealLife
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Let ℝ
D
be
D
-dimensional Euclidean space, and let
. A ‘Euclidean automaton’ is a shift-commuting transformation of
determined by a local rule, analogous to a cellular automaton (CA). In her study of ‘Larger than Life’ (LtL) CA, Evans conjectured that, as their radius grows to infinity, LtL CA converge to a ‘continuum limit’ Euclidean automaton. We prove Evan’s conjecture, and name this family of Euclidean automata ‘RealLife’. We also show that the ‘life forms’ (fixed points, periodic orbits, and propagating structures) of LtL CA converge to life forms of RealLife. We next prove a number of existence results for fixed points of RealLife. Finally, we turn to a more qualitative discussion of the biology of the ‘bugs’ which seem ubiquitous in LtL and RealLife.