Time for some nerd talk.

First, let’s meet the bug formula: $latex bug(x+iy) = x + i* sin(y)$.

Typical fractals iterate the formula $latex z to z^2 + c$. Here the basic fractal formula is combined with the bug formula. There are two ways to combine them.

bug first: $latex z to bug(z)^2 + c$

bug last: $latex z to bug(z^2+c)$

Mathematically the order matters, but for pictures the order makes very little difference. I am not consistent in choosing one or the other. This image happens to use the “bug first” variation.

The image is the “Mandelbrot set” for the combined formula. Technically speaking, if you are not using z^2+c, then it is not the Mandelbrot set. A proper description would be the “parameter space” view. But just this once I will indulge in sloppy language since the process is exactly like creating a Mandelbrot set image, but with the slight change in the formula. Compare to basic fractal.

The image is centered at (-1,0) with width 3.0 and height set to maintain a 1:1 mathematical aspect aspect ratio. (Meaning each pixel represents a square in the complex plane.)