New Evolutionary Model of Life Based on Cellular Automata

New Evolutionary Model of Life Based on Cellular Automata

DOI: 10.4018/978-1-7998-2649-1.ch008
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Abstract

The chapter presents software that implements models of asynchronous cellular automata with a variable set of active cells. The software is considering one of the modifications of the game Conway “Life”. In the proposed model “New Life,” the possibility of functioning of a separate “living” cell is realized, which, when meeting with other “living” cells, participates in the “birth” of new “living” cells with a different active state. Each active state is determined by a code that is formed by the state values of the cells of the neighborhood. Variants of the evolution of the universe based on the surroundings of von Neumann and Moore are considered. This program uses restrictions on the number of “born” cells in order to limit the overpopulation of the universe. Possible goals and objectives to be solved in the use of “New Life” are also considered.
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Conway Game Of “Life”

The English mathematician John Conway invented game of Life in 1970. On the basis of a cellular automata, a universe is presented in which there are two types of cells (“living” and “dead”). Dead cells are represented by a logical “1” state. Eight cells are used to realize the neighborhood (Moore neighborhood).

At the initial moment of the game of life is carried out by the initial filling of all CA cells with “living” and “dead” cells. That is, initially the corresponding cells are set to logical states “1” and “0”. At each time step, a new generation is calculated. To do this, the following rules are used:

  • If a cell has a logical “0” state (“dead” cell) and among neighboring cells three cells have a logical “1” state, the cell goes into a logical “1” state (life is born).

  • If a cell has a state of logical “1” (a “living” cell) and among its neighboring cells there are two or three cells having a state of a logical “1” ((“live” cells), then the cell remains in a state of logical “1” (continues live).

  • If a cell has a logical “1” state (a “living” cell) and among its neighbors there are less than two or more than three cells that have a logical “1” state, then the cell goes into a logical “0” state (“dies”).

The game is terminated according to the following rules.

  • All cells go into a logical “0” state (“die”).

  • At one of the time steps, the state of the CA coincides with one of the states of the CA at the previous time steps.

  • At the next time step, none of the CA cells changes their state.

The first game of life was published in (Gardner 1970). In fact, the game of life comes down to setting the initial state (first population), which during a certain circle of time steps will give the necessary evolution of CA. As a result of the studies, stable forms were obtained that have the following classification.

  • Stable figures are figures that do not change their shape at each subsequent time step.

  • Long-livers are figures that take stable forms through a long number of time steps.

  • Periodic figures are figures whose forms are periodically repeated after a certain number of time steps.

  • Moving figures are figures whose state repeats after a certain displacement.

  • Shotguns are repeating figures, but a moving figure appears.

  • Steam locomotives are moving identical shapes that are left by other permanent or periodic shapes.

  • Eaters are permanent shapes that remain in collision with other shapes.

Currently, there are studies of various modifications of the game of life (Adamatzky 2010; Adamatzky, 2018; Komosinnski, & Adamatzky 2009;10th International Conference on Cellular Automata for Research and Industry [ACRI 2012]; 11th International Conference on Cellular Automata for Research and Industry [ACRI 2014]; 12th International Conference on Cellular Automata for Research and Industry, [ACRI 2016]; 13th International Conference on Cellular Automata for Research and Industry, [ACRI 2018]).

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