Binocular fractal

Written by Paul Bourke
October 2005


The binocular fractal is an illustration of the behaviour of the following complex valued series.

  znm + zn2 + 1
zn+1 = -------------------
  2 znm-1 - z0 + 1


m = 4, The Binoculars. Centered at 1 + 0i



m = 3, The Pliers. Centered at 1.5 + 0i


m = 5, The Sabertooth. Centered at 1 + 0i


Guitar fractal

Written by Paul Bourke
October 2005


The guitar fractal is an illustration of the behaviour of the following complex valued series.

  zn2 + zn
zn+1 = ----------------
  2 znm + z0


m = 2, centered at 0 + 0i