I've been experimenting a bit with what I think is the simplest possible CA-like rule that generates complex patterns and behaviors:
https://eloquence.github.io/elixor/
Essentially, I define an array of size, then walk it in either direction, and XOR the current value in either direction. This gives me a total of four possible universes per universe size. I render all four of these universes by displaying the contents of the array size times, then refreshing.
By choosing a different universe size, I get vastly different patterns. Stability, movement direction, frequency, even speed of movement of the triangles vary. Sometimes fragment structures emerge that add to the complexity.
Does anyone know if the characteristics of this system have already been researched, in terms of:
- classification of the emergent behaviors and structures
- use for universal computation
- symmetry and different forms of projecting the information
- limitations or increases in complex behaviors as the universe size increases
- other aspects of the system, such as oscillation behavior at different sizes
It struck me that many of the behaviors this system generates seem comparable to the so-called elementary CAs, with significantly less complexity in implementation.
Any pointers to relevant papers would be appreciated, as well. :-)