I have been working on a fun art project lately. I call it artomata. I came up with the idea once while I was thinking about cellular automata, and how cool they were. Stanislaw Ulam and John von Neumann first introduced the concept of cellular automata in the 1940s. It is an idea rooted in mathematics but expressed in at least a few natural systems (if not a great many), such as this sea snail shell:
The most famous example of a cellular automaton is Conway’s Game of Life. This “game” (which is not really a game at all, or more technically a zero-player game) consists of a grid of cells. Each cell can be either “alive” or “dead”. When “playing” this game, you can initialize the grid with some alive cells. This is the first “generation”. Each subsequent generation of the game is determined by applying the rules of the game to the current generation. I won’t describe the rules here, but you can read more about it if you’re interested. Basically, whether a cell is dead or alive in the next generation depends on how many of its current neighbors are dead or alive. What’s fascinating about this game is that very complex patterns can emerge from a rather simple set of rules.
The pentaflower consists of a grid of pentagons. The neighbors of each cell are the pentagons with which it shares an edge. The center cell has 5 neighbors, but all others have 3 neighbors. I wrote my code such that the rules can be adjusted, but by default the rule is that a cell is alive in the next generation if it currently has exactly 1 neighbor that is alive. If it has no alive neighbors, or if it has multiple alive neighbors, then it will be dead in the next generation.
You can see the rules in action by going here and incrementing the value of Generation by 1 at a time. When you load the page it will be set to 0. By setting it to 1, then 2, then 3, etc., you can see the progression of the rules through each generation . Additionally, by setting the values of Rings (how big the grid should be) and the colors, many beautiful patterns can be created. You can see a gallery of some patterns I have made on the artomata website. You can also use this page to make pentaflowers of your own.
If you’re interested in learning about how the pentaflower names are generated, you can see this post.
Time permitting, I am hoping to continue the artomata project in my free time, possibly utilizing different geometric shapes and other variations on cellular automata, such as non-binary states.