Abstract
We introduce the Larger than Life family of two-dimensional two-state cellular automata that generalize certain nearest neighbor outer totalistic cellular automaton rules to large neighborhoods. We describe linear and quadratic rescalings of John Conway's celebrated Game of Life to these large neighborhood cellular automaton rules and present corresponding generalizations of Life's famous gliders and spaceships. We show that, as is becoming well known for nearest neighbor cellular automaton rules, these ``digital creatures'' are ubiquitous for certain parameter values.
Highlights
John Conway’s Game of Life (Life) is the most famous example of a cellular automaton (CA), due in part to the fact that its update rule is very simple yet it generates extremely complicated dynamics [BCG82], [Gar70], [GG98]
For Life, as is the case with most CA rules, the initial state has an enormous impact on the resulting dynamics
The Larger than Life (LtL) family introduced a rich collection of two dimensional CA dynamics [Eva96]
Summary
John Conway’s Game of Life (Life) is the most famous example of a cellular automaton (CA), due in part to the fact that its update rule is very simple yet it generates extremely complicated dynamics [BCG82], [Gar70], [GG98]. The gliders are an essential ingredient for the well known result that Life is computation universal [BCG82]. They were the inspiration for the Larger than Life (LtL) family of cellular automata. In addition to being interesting in their own right, some of the LtL rules we describe exhibit nonlinear population dynamics that are prototypes for various spatial models used in fields such as biology, physics, and population ecology As one example, they might provide insights into the design of models to study the extent to which spatial variation in ecological systems influences the ability of a species to survive
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