Abstract
The game of life represents a spatial environment of cells that live and die according to fixed rules of nature. In the basic variant of the game a cell’s behavior can be described as reactive and deterministic since each cell’s transition from an actual state to a subsequent state is straight-forwardly defined by the rules. Furthermore, it can be shown that the alive cells’ spatial occupation share of the environment decreases quickly and levels out at a really small value (around 3%), virtually independent of the initial number of alive cells. In this study we will show that this occupation share can be strongly increased if alive cells become more active by making non-deterministic sacrificial decisions according to their individual positions. Furthermore, we applied signaling games in combination with reinforcement learning to show that results can be even more improved if cells learn to signal for navigating the behavior of neighbor cells. This result stresses the assumption that individual behavior and local communication supports the optimization of resourcing and constitute important steps in the evolution of creature and man.
Highlights
Conway’s game of life [1] is a cellular automaton implemented on an m × n grid of cells
By starting the game of life with a randomly chosen set of alive cells, it can be shown for sufficiently large grid sizes that after a while the occupation share stabilizes on a specific number
We ascertained from the basic tests that n-die games with n < 3 have, if any, a detrimental effect on the game of life since these cells i) would die anyway by the under-population and ii) are highly possible in a shorthanded area and probably important to support neighbor cells not to die by under-population
Summary
Conway’s game of life [1] is a cellular automaton implemented on an m × n grid of cells. By starting the game of life with a randomly chosen set of alive cells, it can be shown for sufficiently large grid sizes that after a while the occupation share stabilizes on a specific number. In each simulation run the number of live cells strongly decreased and leveled out at occupation share values between 1.9% (92 alive cells) and 4.1% (199 alive cells), in average 3.2% (157.6 alive cells) It seems to be independent of the initial occupation share that the final occupation share is around 3%. There is an interesting fact to observe: no matter how high the initial number of alive cells is, the rules of nature of the game of life cause a strong decrease of alive cells down to a very low level of around 3% until it stabilizes. We will show that the final occupation share can be increased by simple fixed pre-“rule of nature” decisions of sacrifice
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