Symmetrica is a cellular automaton with two states. (The name “Symmetrica” comes from the word “symmetry” combined with “CA” for cellular automaton.) As in the Game of Life, the states are referred to as “alive” and “dead.” Each generation, every cell changes state in accordance with the following rules:

  1. If the cell is dead and has 2 or 3 live neighbors in a symmetrical configuration, it becomes alive.
  2. If the cell is dead and has 4 live neighbors which are all orthogonal or all diagonal, it becomes alive.
  3. If the cell is alive and has 2 or 3 live neighbors, it stays alive.
  4. Otherwise, the cell will be dead in the next generation.

In Hensel notation, these rules are abbreviated as “B2-ak3-jnqr4ce/S23.”

In February 2022, I wrote a (now outdated) article with a list of patterns I had discovered the previous summer. Since then, I have investigated Symmetrica further with the help of apgsearch and ikpx2, the full results of which are available on Catagolue. The list of known patterns is now much more extensive, and includes puffers, rakes, and large spaceships.

This website is a catalogue of named objects and their properties. You can click on any image to run it in LifeViewer.

If you are new to cellular automata and don’t know what these terms mean, see here.