This isn’t something new, but a feature that was on my to do list for years after seeing it implemented elsewhere.
The idea is simple. You take a 2D CA and rather than render each step/cycle/update as a 2D image, you add the current 2D cell states as a layer of a 3D stack of cubes. Each slice of the cube is another step in the CA generation.
Once again I must give a shout out to the most excellent Mitsuba Renderer. I would not be able to render these examples with such nicely shaded cubes without it.
This is from another idea I had. Andrew Adamatzky let me know there has been work done using previous states before referred to as “Cellular Automata with Memory”. See these papers by Ramon Alonso-Sanz for other examples of 1D and 2D CAs using memory from previous generations.
This is a totalistic CA that uses the usual 8 immediate neighbor cells as well as the last step’s current cell and 8 neighbors. This gives a total of 17 neighbor cells that can influence the birth and survival of the cells.
I call them “History Dependent Cellular Automata” because they depend on the previous cycles’ neighbor cells as well as the usual 8 immediate neighbor cells.
Here are a few animated GIFS showing some early results. The GIF thumbnails are messy, so click them to see the clear GIFs.
Amoebas 01
Amoebas 03
Sample 01
Space Ships
I also experimented with extending the history back another step.
This gives a much larger search space to find interesting rules within and the majority of rules are random chaos, but here are a few interesting results I stumbled on through random searches. Again, the GIF thumbnails are a mess, so click them to see the clear definition GIF animations.
Feeding Walkers
Space Ships
Surviving Clumps
I also experimented with extending these CA into 3D space. Same principal as 2D but with more neighbors in 3D. Here is an example movie.
These CAs are now included with Visions of Chaos if you want to have a play with them.
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