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.

5D Cellular Automata Settings Dialog

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 Cellular Automaton

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.


3 responses to “5D Cellular Automata

  1. Hi Professor James
    So fantastic work, I want to know how to export each pixel value of a object in visions of chaos, how to develop a new function and add new rules? would you please help me? Thank you.

    • It’s Jason, not James, and I am not a professor. Just an enthusiast of cellular automata and chaos related topics.
      Some of the CA modes (including 5D CA) in Visions of Chaos have export capabilities. You can export to OBJ format file which can be imported into other programs. The OBJ files for large grids can be quite large and cause imports to hang, so start with small 100x100x100 tests first then work up.
      There is no way to code your own new CA types in Visions of Chaos but if you have ideas for new CAs I would like to hear them.

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