How would look a 3D structure with layers corresponding to the cascade of generations of Conway's Life? Such a structure should keep its continuity by nature and probably could beget tree-like or coral-like formations.
One way or another I thought that the simplest way to check it is to build some visualization environment and look at the actual results. So I found a suitable Minecraft-like engine and gave it a try.
As a basis for the research of the structures in question, I took the Michael Fogleman's code which is the python open-sourced clone of Minecraft. I added a simple interpreter of Conway's Life and made several visualization control improvements.
For the first experiments, several patterns were chosen:
- "R-pentomino", diehard", acorn"-- as well-known patterns which lead to complex non-trivial evolution from a simple starting seed.
- "Max spacefiller" -- as the source of the fastest known growth rate.
- "Onion rings" -- as an example of the agar decay process.
The support of the simple pattern description format brought the ability to promptly check the evolution of any desired pattern. The frames recording mode opened the easy way to generate movies. In order to enhance the expressiveness I added the colouring scheme based on a cells' future destiny: the neutral gray color corresponds to cells, which will stay alive in the next generation; the dark gray is for lonely dying cells; and the light gray is for the overpopulated ones.
Now, you are able to:
- watch several ConwayTree movie clips on YouTube,
- checkout and run the ConwayTree code from the github project