Strive or die: the game of life

One-dimensional cellular automata were fun. Now what about different dimensions? If such a diversity of pattern could be generated with 1D automata, how much more complex and beautiful should be higher dimensions?

Two-dimensional cellular automata are often called life games as they can represent the evolution of a population, each cell dying or striving depending on their own state and on the state of the surrounding cells. Here are some examples. The first one shows the evolution of a single cell according to the following simple rules: if a cell has one and only one neighbour alive, it lives; if it is isolated, it keeps its state; if it has more than one neighbour alive, it dies. We can see that in the first step, the cells surrounding the initial cell will become alive. In the second step, they will all die, but four corner cells will become alive. And it goes on, points generating squares, and squares generating points. The two next examples are variations with several colors. The last example is the simulation of the evolution of a population. Starting with a random population distribution, the population evolves with the following rules: the cell dies if it has less than two neighbours, or more than three; its state is unchanged if it has two neighbours; it lives if it has exactly three neighbours. With these simple rules, it is fun to watch the population grow, stabilize, or die out depending on the initial state.

Now, let's play the game! First, press the start button of the calculator to see what happens, then try to vary the parameters.

Usage: the initial population is chosen by clicking the cells or by selecting the "Random init" checkbox. You can edit the rule on the left that gives the correspondence between the sum of the neighbour state and the current cell state to the next cell state. The red squares at the left of the rule scroll pane shows which cells are included in the sum. You can change the symmetry of the evolution by changing the cells included. Try for example to exclude the corner neighbours. Clicking on the random rule button generates a new rule randomly. When "full screen" is selected, a new screen-size window opens to display the cellular automaton. In this mode, press any key to stop it. Finally, the number of color and the number of neighbours can be changed with the parameters shades and extent. Caution: changing extent or shades is memory consuming and can cause the program to fail - or your browser to crash.

Now continue with animal patterns.

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This page was created on 5/29/2001 by Mite.
Copyright May 2001 by Mite.