While avoiding grading a quiz over the weekend, I sat down and started playing with Julia sets of higher degree polynomials a bit. Last week’s Mandelbrot fractal was centered in an area that gave rise to a pretty stunning Julia set, and I was hoping to find something analogous in a higher degree creature.
Alas, I haven’t found it yet, but while messing with a fifth degree Julia set, I found today’s structure. I thought it looked something like a sand dollar—it has the five-fold rotational symmetry[ref]And the fact that five is a Fibonacci number, I am led to believe, is not a coincidence, though I don’t know enough about how sand dollars grow to give a definitive answer.[/ref] and radial structure that one might expect. After some experimentation with the color palette, I came up with the image above (which is a detail from an 11.8 MB picture).
My plan is to keep looking for multi-fold dragons, but until I find one, I hope this suffices.