Orbit trap fractals
A so-called orbit trap
is a geometrical object in the complex plane that is used to generate a fractal. When using an orbit trap, the fractal is formed of slightly distorted copies of the orbit trap.
When using an iterative function to generate the Mandelbrot set or a Julia set, each iterated point is generated along a so-called orbit. The distance to the orbit trap from each point on the orbit is calculated, then the minimum distance is used to colour the original point. The iteration continues for a fix number or steps, or until a point on the orbit gets sufficiently close to the trap - in which case the orbit gets trapped.
In the picture below, a point, a cross, a square, and a circle are used as orbit traps.
Make orbit trap fractals at: http://www.malinc.se/m/OrbitTraps.php