An Artistic Rendering Method for 3D Fractals

In this paper, we present a novel method to render colorful 3D fractals based on so-called color-control sphere (CSS) and our improved escape-time algorithm. In the method, each point, called parameter point, in parameter domain is first judged whether it is an escape-point or not by an iteration loop, under the governing of a discrete dynamic system. Once the iteration loop is exited, an orbiting point corresponding to the parameter point is then mapped to a mapped-point in CCS and the distance from the mapped-point to the center of CCS is evaluated. Subsequently, a color for rendering the parameter point can be obtained by employing a predefined color-control function in CCS with respect to the distance. Finally, all surface points, which are taken as a set of initial points of the discrete dynamic system, of arbitrary shape embedded in the parameter domain are rendered with their corresponding colors. As a result, a pseudo-3D fractal can be archived on the 3D surface.