A phoenix is an oscillator in Conway’s Life where every cell dies in every generation. The smallest example is Phoenix 1, which oscillates with period 2 and has a constant population of 12:
All known finite phoenices have period 2, and Stephen Silver proved in 2000 that there cannot exist a finite phoenix of period 3. Alex Greason more recently proved the non-existence of any phoenix (finite or infinite) with period 3 or 5.
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[ 2.8 ms ] story [ 23.6 ms ] threadA phoenix is an oscillator in Conway’s Life where every cell dies in every generation. The smallest example is Phoenix 1, which oscillates with period 2 and has a constant population of 12:
All known finite phoenices have period 2, and Stephen Silver proved in 2000 that there cannot exist a finite phoenix of period 3. Alex Greason more recently proved the non-existence of any phoenix (finite or infinite) with period 3 or 5.