Bugs #4

Bugs Fractal 79

Here is the same image as yesterday, but with “black inside” turned off.

Traditionally for fractals only the escaping points are colored, and the color indicates how quickly the point escapes. The non-escaping, or “inside” points are colored black. For traditional fractals, the insides are boring. The orbits of the points in the non-escaping region flow towards a single fixed point, or an attracting cycle. A solid inside color helps shifts the viewer’s focus to the swirls surrounding the fractal body.

With non-traditional fractals, especially fractals based on non-holomorphic functions, the inside area is more interesting. The orbits can bounce around in chaotic fashion, never settling into a fixed point or cycle. It is not easy to find a meaningful way to color such regions. But that makes it all the more rewarding when you discover a way to visualize the area.