Evolution of Cellular Automata

In this section we will describe the pattern formed by evolving cellular automata from simple species. The seed is composed of a zero site background, a single non - zero site, or a small area containing a few non - zero sites. As cellular automata grow from this initial condition, models of various physical phenomena and other phenomena should be obtained. One example is crystal growth. The cellular automata lattice corresponds to a crystal lattice, and the non-zero position indicates the presence of a crystal atom or region.

A more complicated cellular automaton is the one-dimensional global cellular automaton of the nearest color. In such an automaton, the average of adjacent cells determines the evolution, and the simplest and most important example has color. For these automata, the set of rules describing behaviors can be encoded as a number - a number called a "code". The above explains ternary () code 912 automaton rules and 300 steps. In two ways, the most famous cellular automaton is Conway's life game discovered by J. H. Conway in 1970 and advertised in the Scientific American column of Martin Gardner. The game of life is a whole cellular automaton with binary () with a large neighborhood range. Life-long continuous game calculation was originally done by hand, but the computer revolution occurred soon, and a wider model for research and dissemination became possible.

The simplest one dimensional cellular automaton basic cellular automaton has two possible values ​​for each unit (0 or 1), and the rule depends only on the nearest neighbor value. Therefore, the evolution of a basic cellular automaton can be completely explained by a table that specifies the state a given unit has in the next generation, based on the value of the left cell, the value and value of the cell itself. On the right side of the cell Since there are binary states in the three cells adjacent to a given cell, there is a basic cellular automata in total and each can be indexed with 8 bit binary numbers (Wolfram 1983, 2002). For example, the table showing the evolution of rule 30 () is shown above. In this figure, the possible values ​​of three adjacent cells are displayed in the top row of each panel, and the value of the result generated by the middle cell in the next generation is displayed in the lower center.