ChristensenSet.jl: Gallery
A computation of Christensen sets in Julia.
What is Christensen's set?
Let us consider a finite set of complex numbers $K$ and a positive integer $n$. Then the Christensen set $C_{K, n}$ is the set of all roots of univariate polynomials with coefficients from $K$ and degree at most $n$. It is a subset of the complex plane and it is easy to visualize its density.
Pictures below were generated by Julia package ChristensenSet.jl. I have chosen three simple and beautiful examples. In each you can see an overall picture of the fractal and then some selected parts in more detail.
For more information about this type of fractal set see John Baez's article and Dan Christensen's experiments.
Example 1: $K = \{ -1, 1 \}$ and $n = 25$
There are in total $3\,221\,224\,897$ roots.
Example 2: $K = \{1, 3\}$ and $n = 22$
There are in total $352\,321\,541$ roots.
Example 3: $K = \{-1, 1, i, -i\}$ and $n = 22$
There are in total $1\,043\,915\,665$ roots.
