Complex Iteration

For example, suppose (a, b) = (1/2, -1/2) and (x₀, y₀) = (0, 0). Then

x1 = x02 - y02 + a = 02 - 02 + 1/2 = 1/2

y1 = 2*x0*y0 + b = 2*0*0 + (-1/2) = -1/2

Next,

x2 = x12 - y12 + a = (1/2)2 - (-1/2)2 + 1/2 = 1/2

y2 = 2*x1*y1 + b = 2*(1/2)*(-1/2) + (-1/2) = -1

Then,

x3 = x22 - y22 + a = (1/2)2 - (-1)2 + 1/2 = -1/4

y3 = 2*x2*y2 + b = 2*(1/2)*(-1) + (-1/2) = -3/2

and so on.

Return to Complex Iteration.