Generate complex fractals and mandelbrots with aesthetic visual effects

The Julia and Mandelbrot sets are two of the most famous fractals. There has been extensive research done in visualizing them in two dimensions and three dimensions because of their interesting mathematical properties and corresponding visual beauty. In this work we aim to visualize the Mandelbrot and Julia sets in three dimensions by using ray tracing – the nominal algorithm for visualizing these sets. In this paper we describe the different methods – in conjunction with ray tracing – used for rendering the Julia and Mandelbrot sets. These methods include 3 types of quaternion math, 2 types of normal approximation used for coloring and the animations provided to view the full complexity of these wonderfully complex fractals.