5D Cellular Automata

After 4D cellular automata the next logical step was to another dimension and see what 5D cellular automata can do.

If you are familiar with lesser dimension CAs then 5D is just an additional value in the cell arrays. 3D uses [X,Y,Z], 4D uses [X,Y,Z,W], and for 5D you use [X,Y,Z,W,V]. 5D extends the number of immediate Moore neighbors of each cell to 242 (3^5-1) (4D has 80, 3D has 26).

The settings dialog gets even more checkbox chock-a-block as follows.

Looping through the additional dimension makes calculating these 5D CAs much slower than 4D and lesser dimension CAs to process. I was able to go up to 50x50x50x50x50 sized arrays, but beyond that was too slow for my patience.

Coloring these CAs use the same methods as the 4D cellular automata. The only change is for the “4D density” display method. Rather than using the density of the 4th dimension to show a cell color, the 5D version uses the density of both the 4th and 5th array dimensions for color.

I have not found any really interesting 5D CA rules yet. Because they are so much slower and the search space is so vast, trying multiple random rules really needs to fluke it to find an interesting result. For now here is a simple example starting from a single active cell. Click the image to watch a short animated GIF.

5D CAs are now available in Visions of Chaos. If you do happen to find any interesting 5D CA rules, let me know. I asked the same for 3D and 4D and got no responses, but who knows, maybe you reading this now will be the one to find a bunch of new and interesting rules for higher dimension cellular automata. Stay tuned for a YouTube sample movie once I get enough interesting 5D rules.

Jason.