beanLife3D is a mathematical screensaver that lets you watch cellular automata, evolve, grow and interact.
Billions of beautiful creatures (often of symmetry) can emerge with some fantastic properties some may establish a stable state and live until they are disturbed by other creatures in the tank, others may evolve only to annihilate themselves.
Colonies may merge together, move around, grow on the walls, extend arm-like protrusions, launch missiles and a lot more.
If you buy a registration key you can set the rules of the universe yourself, and explore the multitude of different possibilities.
The free version comes with a fixed set of rules and adjustable grid size.