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

AbstractComputer 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,fα, c(z)=zα+c, where α is a real number, and the Newton form of an equation, $$\exp \left( { - \alpha \frac{{\zeta + z}}{{\zeta - z}}} \right) - 1 = 0$$ where ¦ζ¦=1 and α>0.

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