Simulate a 1D Game-of-Life-ish Model
05AB1E, 14 13 10 9 6 bytes

Based on Shaggy's Japt solution

F©Á®À^


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F                  # repeat n times:
 ©Á                #  the list, rotated right
   ®À              #  the list, rotated left
     ^             #  xor (vectorizes)




Unnecessarily clever 9-byte solution:

F¥DO.øü+É


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F                  # repeat n times:
                   #  (examples given for the initial state [0, 1, 1, 0, 1])
 ¥                 #  deltas of the list ([1, 0, -1, 1])
  D                #  duplicate
   O               #  sum (1)
    .ø             #  surround ([1, 1, 0, -1, 1, 1])
      ü+           #  pairwise addition ([2, 1, -1, 0, 2])
        É          #  modulo 2 ([0, 1, 1, 0, 0])