Generations rules are Life-like rules with extra fading states, and Brian's Brain is the best known of them. A live cell (blue) that fails to survive does not die at once: it fades through a chain of dying states (red to pale) and only then becomes empty, and a dying cell can neither live nor count as a neighbor. The rule reads B (neighbor counts that give birth) / S (counts that let a live cell survive) / C (total number of states, counting empty and live). Pick a rule, or type your own such as B2/S345/C4. Brian's Brain is B2/S/C3: an off cell fires if exactly two neighbors are firing, and a firing cell always dies, so nothing ever stays on. Let a cell fire when two or more neighbors are firing and keep a long fading tail (B2345678/S12/C8) and you get an excitable medium, the same idea as heart tissue or the Belousov-Zhabotinsky chemical reaction: a wave of firing cells travels outward and leaves a fading tail that cannot fire again, so waves never cross and bend into spirals. Start those from Random states.

Generations rules were collected in the MCell and Golly programs. Only cells in the live state count as neighbors, so the fading tails never cause births, but a tail cell blocks its square until it has faded away. With three states you get Brian's Brain, devised by Brian Silverman, who also invented Wireworld: a random start boils for a while and settles into a sea of small spaceships that glide in all four directions and collide. The two spaceships in the Start menu are tiny seeds that run away from their starting point forever under that rule (under other rules they do something else). With more states, the long fading trails turn small gliders into comets. The excitable-medium presets are rules I found by searching for ones that keep wavefronts moving from a random-states start; in my tests they form spiral waves, and other settings of the same kind may too. With eight neighbors the spirals are somewhat square. Not every rule stays active: a random start can burn out quickly, so press Random again. The preset names and numbers are as I remember them from those programs, so treat the names as labels, not as a reference.

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