Mandelbrot Orbit Traps

These images were made by the Fracture screensaver.

Like the previous category of images, these are images of the Mandelbrot Set. However, these images use a special coloring technique called "orbit traps". Conceptually, an orbit trap is an object that is "placed" into the same mathematical environment as the fractal itself. Due to the nature of the mathematics, the orbit trap object is copied many times, while being scaled, rotated, and stretched in all sorts of ways. So a single orbit trap object can result in an image containing what appear to be a great many objects.

In more mathematical terms, an orbit trap is a test that can be applied to complex numbers. One possible test, for example, might be "is this complex number within 0.5 units of distance from the point 0.75 + 0.25i or not?" This example orbit trap test would correspond to an orbit trap object that is a disc of radius 0.5 with its center at (0.75, 0.25). If the test is "true" for the point z at any time as it travels around the complex plane over the course of the iteration of the Mandelbrot Set's generating function z ← z2 + c, then the point z is considered "trapped" by the orbit trap. The original point c, which through iteration became the point z that was trapped, is colored in some way associated with the orbit trap. The coloration is based not only upon which trap was hit, but on "how true" the trap was (how far from the center of the orbit trap disc the point z was, for our example), what iteration the trap was hit on, what other traps were hit in the course of the point c's full iteration, and other factors.

All of these images are copyright © 2001 Ben Haller. Personal use of these images is allowed; all other use, including any kind of redistribution or reproduction of these images, is forbidden without the express, written consent of Ben Haller.