I just now convinced myself that the spooky blinker is a valid oscillator. On Tue, Apr 21, 2020 at 7:10 PM Allan Wechsler <acwacw@gmail.com> wrote:
While musing about searching for Life patterns with particular properties, I had an idea for a Lifelike cellular automaton rule that surely must have been invented before. So I'm hoping somebody can give me references.
The rule has three states. Two are Life's existing "dead" and "alive", and any situation involving only these states evolves exactly as in Life.
The third state is like a quantum superposition of "dead" and "alive". Call it "spooky".
The principle is this: a pattern P with spooky cells corresponds to a set L(P) of ordinary Life patterns. A Life pattern belongs to the set if it agrees with P on all non-spooky cells.
A cell is alive in P', the successor of P, if for all patterns Q in L(P), it is alive in Q'.
Similarly, it is dead in P' if it is always dead in Q' for all Q in L(P).
A cell is spooky in P' in all other cases, that is, if it is sometimes alive and sometimes dead in Q' depending on the choice of Q from L(P).
Spookiness is ignorance. Sometimes it disappears completely -- an isolated spooky cell in empty space dies is one step.
This is a well-defined automaton, and its rules can be completely stated; an example is "a live cell with two live neighbors and one spooky neighbor will stay alive", an "a dead cell with three or more spooky neighbors and no live neighbors becomes spooky".
Has anybody implemented this rule for Golly? (I am a Golly tyro and don't know the rule-specification language yet.)
Does this rule have any non-trivial interesting patterns? Like -- does it have any oscillators involving spooky cells? Any spaceships? I know it has at least one still-life: the spooky block is stable.