Take three numbers in the complex plane, z₁, z₂, z₃ and consider the Julia set for the Newton iteration process for solving (z - z₁) (z - z₂) (z - z₃) = 0. If we move z₁, z₂, z₃ about in the plane, we get a changing Julia set.

The Julia set for the Newton iteration for solving z³ - 1 = 0. Here we zoom in by a factor of one million to watch the self-similar endlessly repating structure of the set.

Given a pair of numbers (a,b), let us say that an (a,b)-polynomial is a polynomial in which every coefficient is either a or b. There are 2^(n+1) such polynomials of degree n, provided a and b are not equal.

For any given pair (a,b) we can draw all the zeroes of all the (a,b)-polynomials of degree at most 11, where zeroes of lower degrees are represented by larger circles. Let us call this an (a,b)-image.

The animation shows (a,b)-images as the pair (a,b) moves in a line segment from (1,1) to (-1,1). In other words, a changes from 1 to -1, while b stays fixed.

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