Newton’s Fractals on Surfaces via Bicomplex Algebra

What is it about?

We present a method for generating interesting patterns over 3D surfaces by defining a generalization of Newton's fractal in 4D space, using bicomplex numbers. We found that these patterns can be applied in texturing to define beautiful decorations and material masks, and they can also be efficiently computed by parallelizing the process on GPU hardware.

Featured Image

Photo by Christian Liebel on Unsplash

Photo by Christian Liebel on Unsplash

Why is it important?

Defining textures through fractals allows for high-quality, photorealistic patterns in several settings. While using fractals for our proposed applications is not a novel idea, Newton's fractal had yet to be applied in the 3D setting. Furthermore, since bicomplex algebra supports a 4-dimensional coordinate system, the fourth dimension can be exploited to animate the resulting patterns.