User:Saka/Inner-only totalistic Cellular Automaton
Inner-totalistic rules are a family of rules brought into existence by Saka.
Inner-totalistic rules are rules where a cell's state in the next generation is solely based on the state of the cell itself. Because of this, there is no transfer of any information between neighbors.
The notation of inner-totalistic CA can be described as 0-c'/1-c', where 0 and 1 are the cell's current state and c' is the cell's state in the next generation.
There are four 2-state inner-totalistic CA, listed and described below:
Everybody Dies is an inner-totalistic CA where every living cell dies. It can be noted by 0-0/1-0, which means that state 0 turns to state 0 and state 1 also turns to state 0. This can be emulated using the rule B/S. This is by far the most uninteresting rule, as nothing can survive past the first generation. However, it might be of note that every pattern (Aside from the vacuum, but it is debatable whether a vacuum counts as a "pattern",) in this rule is a Garden of Eden.
Everybody Lives is an inner-totalistic CA where every cell becomes alive. It can be noted by 0-1/1-1, which means that state 0 turns into state 1 and state 1 also turns into state 1. It can be emulated using the rule B012345678/S012345678. The entire universe will become a giant still life in exactly 1 generation. Every pattern in this rule, except a completely filled universe, is a Garden of Eden. However, because of the nature of infinity, it still means that there are infinite Gardens of Eden in this rule. Another property of the only still life in this rule, the filled universe, to note, is that it has infinite unique parents, but no grandparents, that is, apart from itself (which becomes itself in two generations), since it is a still life.
Nothing Happens is an inner-totalistic CA where all cells stay as they are, forever. This rule can be noted as 0-0/1-1. It means that state 0 turns into state 0 and state 1 turns into state 1. This can be emulated using B/S012345678. This rule is interesting because it has infinitely many still lives as every single pattern is a still life. Since every pattern is a still life, every pattern has only one parent, itself.
Awful Strobe is an inner-totalistic CA where each state changes to the opposite state, creating a horrible strobe effect. This rule can be noted as 0-1/1-0. This means that state 0 turns into state 1 and state 1 turns into state 0. It can be emulated using B012345678/S. In the rule, the entire infinite universe is always a giant period 2 oscillator and phoenix, and every pattern is a unique period 2 phoenix. Unlike other inner-totalistic cellular automata, no pattern is a Garden of Eden since everything is a period 2 oscillator and thus must have a parent (Which is also a phase of itself).
Thank you, dvgrn.