A number of different semitotalistic rules for the 3D rectangular Moore neighborhood were investigated.
It was popularized by A. K. Dewdney in his "Computer Recreations" column in Scientific American magazine.
In every step of Conway's Game of Life follows four rules: These events may be simplified in a way where we emphasize a given cells next state based on the range of the number of that cell's neighbors This reworking of the rules allows us to formalize them.
as the number of living neighbors required to prevent a currently living cell from dying, which upper and lower limits
as the number of living neighbors required to create a new living cell, with upper and lower limits
For example, Conway's Game of Life has a transition rule
[1] We can use this transition rule to create different variants of the Game of Life.
results in an explosive variant of the Game of Life called 3-4 Life, and one of the earliest studied variants of the famous automaton.
Because of the transition rule's complete independence from the number of dimensions, we may translate the transition rule into the third dimension.
Unsurprisingly, many of the transition rules either decays too quickly, expands too quickly, or doesn't create anything interesting in a given "primordial soup" seed (ex: gliders, spaceships, blinkers, etc.)
We loosely formalize a Game of life like so: An automaton with a transition rule
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