## Artists

## Statement

I find beauty in the way that relatively simple mathematical equations can give rise to complexity, and I render this complexity as images. In this exhibition I use techniques from my paper "Extending Mandelbox Fractals with Shape Inversion". The Mandelbox is a class of escape-time fractals that use a conditional combination of reflection, spherical inversion, scaling, and translation to transform a point under iteration in n-dimensional Euclidean space. For this artwork I use a 4D version of the Mandelbox algorithm, which I modified to replace spherical inversion with a more generalized type of inversion that allows non-spherical inversive shapes, thus enabling exploration of new kinds of fractals.

## Artworks

This image is a 2D rendering of a 3D slice through a 4D Mandelbox fractal where 4D spherical inversion is replaced by shape inversion using a shape that is a linear blend of a 4D hypersphere (glome) and a 4D hypercube (tesseract). Colors are based on the path each point in the Mandelbox takes under iteration. I like to think the result is reminiscent of the patterns of concentric circles, squares, and gates of traditional mandalas.