Another short code I wrote in Mathematica language was accepted by The Wolfram Demonstrations Project. The Demonstration shows the evolution of two elementary cellular automata (CA) sharing several cells. CA are often treated as isolated systems with simple cyclic or Dirichlet boundary conditions. Realistic systems, in contrast, interact with the environment through a boundary. Boundaries can be as simple as solid body surfaces, as complex as walls of living cells, or even have non-geometric nature as the boundaries of social systems. A boundary, having an intricate structure and being a coupling link to the environment, can strongly influence the system dynamics. Here two elementary CA colored red and blue interact via a boundary consisting of black shared cells. The configuration of coupling is schematically shown on the image at the lower-left corner of the graphic. Even the single cell boundary can significantly alter the dynamics of CA. If the black overlap is made significantly large, it can be considered as a 2-color range-2 CA interacting with two elementary CA. The boundary in this case is the line separating CA of different color. The CA exchange information via the bordering cells. The Demonstration also shows how larger neighborhood CA patterns arise from the multiple action of smaller neighborhood CA. Click on the picture below for more technical description and to play with the program. Click on the YouTube icon to view a short video of the demonstration.
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Vitaliy's bookshelf: read
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