Life: Created or Evolved?
Given the state of a square Game of Life grid, determine whether it could have evolved from any previous state, or could only have been created. That is, identify whether the state is a “Garden of Eden” state.
A square grid of states, with 1 indicating “alive” and 0 indicating “dead”. You may choose any two distinguishable symbols instead of 0 and 1 if you wish.
The side length of the grid will not be zero, but may be any natural number 1 <= N <= 20.
Any or all of the cells outside the input grid may be alive at this generation, and any or all of them may have been alive in the previous generation. The universe to be considered is infinite, so there are no boundary conditions. The edges of the input are not the edges of the universe. Specifically, the grid does not wrap.
The input may be in the form of a row delimited string, or a single string. If you wish, you may take the side length or the area of the grid as an additional input (before or after the grid).
Acceptable input formats:
010,101,010 010101010 010 101 010 3 010101010
“Created” if there is no possible previous state (including states larger than the input grid) that would lead to the input state on the next generation.
“Evolved” if there exists at least one possible previous state (including states larger than the input grid) that would lead to the input state on the next generation.
You may use any two distinguishable strings or numbers instead of “Created” and “Evolved” if you wish.
Note that the possible previous state need not be distinct from the input. If a state has itself as the next generation, then it should be considered evolved.
010 101 010 Evolved 0101110100 0010101001 1011100110 0101111101 1001001111 1111001001 1011111010 0110011101 1001010100 0010111010 Created
The created test case is taken from Achim Flammenkamp’s Game of Life Page.
Thanks to trichoplax for writing this challenge and I adopted it from here