Use of potential functions in 3D rendering of fractal images from complex functions

Abstract

Computer graphics is important in developing fractal images visualizing the Mandelbrot and Julia sets from a complex function, Computer rendering is a central tool for obtaining nice fractal images, We render 3D objects with the height of each complex point of a fractal image considering the diverging speed of its orbit. A potential function helps approximate this speed, We propose a new method for estimating the normal vector at the surface points given by a potential function. We consider two families of functions that exhibit interesting fractal images in a bounded region: a power function, f(alpha,c)(z) = z(alpha) + c, where alpha is a real number, and the Newton form of an equation, exp (- alpha zeta + z/zeta - z) - 1 = 0 where \zeta\ = 1 and alpha > 0.