Consider the Julia set given in Figure 13.1(a). Take the mapping zn+1 =

z2n

+

c, where c = −0.5 + 0.3i.

(a) Iterate the initial point z0 = 0 + 0i for 500 iterations and list the final 100. Increase the number of iterations. What can you deduce about the orbit?

(b) Iterate the initial point z0 = −1 − i and list z1 to z10. What can you deduce about this orbit?