Range question in fractal generated from infinite sum

Ballaw

Here's a problem description for generating a fractal:

The program will use the position of the mouse to set the value of a complex number of the form v = (a + bi). The program will then draw a large collection of points (or small circles) that are positioned at the locations given by sums of powers of this value v. In particular, you can calculate truncated sums of an infinite series of powers of v:

1.0 -- 0