Tenth Homework Set Answers

5. (a) Note that c = -1 works:
  z0 = 1
  z1 = 0
  z2 = -1
  z3 = 0
  z4 = -1
  z5 = 0
The values eventually cycle between -1 and 0, hence do not run away to infinity, so z0 = 1 does belong to the c = -1 Julia set.
 
(b) Note that c = -1 works:
  z0 = -1
  z1 = 0
  z2 = -1
  z3 = 0
  z4 = -1
  z5 = 0
The values cycle between -1 and 0, hence do not run away to infinity, so z0 = -1 does belong to the c = -1 Julia set.
 
(c) Note that c = -2 works:
  z0 = 2
  z1 = 2
  z2 = 2
  z3 = 2
  z4 = 2
  z5 = 2
The values stay at 2, hence do not run away to infinity, so z0 = 2 does belong to the c = -2 Julia set.

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