Seeds/Snippet

Seeds is a Life-like cellular automaton in which a new cell is born when it has exactly two live neighbours, and live cells never survive to the next generation. Even though all the living cells die in every generation (turning every pattern into a phoenix), most patterns are still exploding quadratically.

On October 30, 2020, Peter Naszvadi proved that Seeds is Turing-complete on an infinite, periodically-tiled grid by constructing a Rule 110 "unit stripe".

No still lifes can exist in this rule, due to the absence of survival conditions. Known oscillator periods include 2, 3, 4, 5, 6, 8, 12, 15, 20, 24, and 40. The five smallest oscillators are duoplet (2 cells, p2), shiplet (3 cells, p2), radar (4 cells, p4), lever (4 cells, p4) and anchor (4 cells, p4).

With B2, the Seeds rule allows spaceships to travel at the speed of light. The three smallest ones, known as photons, have a period of 1 and consist of only 4 cells each. Larger lightspeed spaceships with higher periods are also known. There also exist 3c/5, c/2, c/4, and c/5 orthogonal spaceships and c/3 and c/4 diagonal spaceships.