Before moving on, I wanted to zoom out on the graph of the chi function, to really show the fractal behavior.

Note that while my fractal "star" is finite in size and complexity, the true chi "star" grows more elaborate as we zoom further out, and grows to infinite size and complexity. Someday I might try to do better justice to this graph by taking it a few iterations further before performing several hundred iterations. As it is, the graphs here represent the detail from about 8 iterated logarithms, give or take, and they took over a day to assemble. I've already far exceeded the limits of machine precision and had to be a little clever to continue the graphs accurately.

Note that while my fractal "star" is finite in size and complexity, the true chi "star" grows more elaborate as we zoom further out, and grows to infinite size and complexity. Someday I might try to do better justice to this graph by taking it a few iterations further before performing several hundred iterations. As it is, the graphs here represent the detail from about 8 iterated logarithms, give or take, and they took over a day to assemble. I've already far exceeded the limits of machine precision and had to be a little clever to continue the graphs accurately.

~ Jay Daniel Fox