Unveiling the Grid: What Shape Reveals About Cellular Behavior
If you’ve been following textbook examples of cellular automata, you may have noticed that for some rules, especially rules like 252, 253, 254 with black and white colors, part of the screen becomes completely colored black. You might not have noticed this in any of my previous posts. Let me explore this concept in this post.
In the grid chosen for cellular automata, each cell has a square or rectangular shape. Before starting the rule generation, all cells have values of 0, except for the starting line with the initial points.
When cells have a bit value of 0, they appear white. That’s why the whole screen appears blank (white) in the beginning. When a cell’s bit value turns from 0 to 1, we change the white cell to black.
Of course, if you enjoy experimenting like I do, you can start with a black background and turn cells white when they’re activated.
In my previous posts, I used a circle instead of a rectangle for most examples, and I’ve been using multi-color palette gradients. Because of this, you may not have noticed entire regions changing colors.
Let me show you the results of using a rectangular grid instead of a circle, using Rules 254, 225 and 215.
Rule 254
Rule 225
Rule 215
Beyond circles (with their gaps around), which unlike rectangles (or squares) do not form a tightly packed grid, one can explore non-equilateral triangles, pentagons, and many other polygons. There are numerous shapes to investigate, each offering new insights. These simple cellular automata, now shining with colors, have many new lessons to teach us through these alternative geometric shapes.
Written by Iohannes — John Samuel.
