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The Hexagonal Game of Life

This is a cellular automaton based on Conway's game of life, but played on a hexagonal grid. Each rule determines whether a cell will be occupied (red) or empty (gray); if the configuration of the cell and its neighbors rotates to one of the circled configurations, it will be occupied in the next generation, otherwise not.

The user can start with new rules and new population, or continue or stop the present calculation, get a new random population, or clear the present one, get a new random set of rules or clear the present set, change the number of generations per calculation, the delay time between generations in thousandths of a second, or the size or density number of configurations, every set-up is periodic, although usually of extremely large period; the Period button seeks to find the period. In looking for a period, it will speed things up to make th delay 0 and toggle to No Display.

You can also click on a cell to switch from occupied to empty or back, or on a rule to activate or deactivate it. Some browsers do not recognize clicking cells, so there is a Cell button to input the coordinates of a cell. The first coordinate goes left to right, while the second goes down the 60 degree line toward the right.

The height and width of the board are adjustable. To solve the problem of edges, the left and right sides of the field are adjacent, as are the top and bottom, although in the latter case there is a shift. A zero shift corresponds to identifying the ends of a line going down 60 degrees to the right. If the height is even, then a shift of half the height would identify a point with on the same vertical.

Since there are finitely many configurations, there will eventually be repetition, although generally after far too long a time to find it. But for those cases where it may be tractable, I included a button called "period" to search for it. In most cases, this effectively means continue forever.

My favorite set of rules is just below. Try it with a simple triangle of three adjacent points, or with some random starts, for example. Another consists of the single rule that an empty space with one neighbor comes to life. Try this on a square board, starting with a single point at the canter or at a corner. There are other interesting possibilities, of course, and I would appreciate hearing about your favorites at holzsager@rcn.com.


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