Cellular Automata Cellular automata are discrete dynamical systems whose behavior is completely specified in terms of a local relation. A cellular automaton consists of an array of cells, each of which is allowed to be in one of a few states. At the same time, each cell looks to its neighbors to see what states they are in. Using this information, each cell applies a simple rule to determine what state it should change to. This basic step is repeated over the whole array, againand again. The system's laws are local and uniform. The system was invented in the 1940's by John von Neuman and Stanislaw Ulam at Los Alamos National Laboratory in New Mexico.
The Most Famous Cellular Automaton Is: JOHN CONWAY'S GAME OF LIFE devised in 1970 by John Horton Conway, a young mathematician at Gonville and Caius College in Cambridge. Conway knew that a cellular automaton with simpler capabilities could be created using only two states - dead or alive. This was different from von Neuman's which had 200,000 cells in any of twenty-nine states-this was too complex.
STANDARD RULES FOR THE GAME OF LIFE
1. STASIS: A cell with exactly 2 neighbors will remain as is in the next generation. (If off, it stays off. If on, it stays on)
2. GROWTH: A cell with 3 neighbors will live (turn "on") in the next generation.
3. DEATH: A cell with less than 3 neighbors will die (turn "off"). A cell with more than 3 neighbors will die (turn "off").
Conway tried many different numerical thresholds for birth and survival. He had THREE OBJECTIVES:
1. He wanted to ensure that no simple pattern would grow without limit. it should not be easy to prove that any simple pattern grows forever.
2. He wanted to ensure that some simple patterns do grow wildly. There should be patterns that look like they might grow forever.
3. There should be simple patterns that evolve for a long time before stabilizing. A pattern stabilized by either vanishing completely or producing a constellation of stable objects. Despite the simplicity of the rules governing the changes of state as the automaton moves from one generation to the next, the evolution of such a system is complex indeed. In real life, matter (energy) cannot be created or destroyed. However, no such restriction applies in LIFE. The amount of "matter" in the LIFE universe can fluctuate arbitrarily.
In our Java model of the Game of Life:
1. An empty cell signifies that the cell is dead or "off", a cell filled with a color is alive or "on".
2. You can use either the standard number of 3 for the game of life or you can choose numbers 2 through 6 from the pop-up menu. This number determines the number of neighbors needed for a cell to survive. The first generation is randomly produced. But, for the sake of comparison, that first generation does not change when the user changes the variable number from the pop-up list.
3. You cannot change the rules for Stasis , Growth or Death. only thenumbers of neighbors which determine Stasis , Growth or Death.