I just got back from the amazing Bridges 2018 math/art conference in Stockholm. I gave a talk presenting results from my paper “Extending Mandelbox Fractals with Shape Inversions”, which was published in the conference’s peer-reviewed proceedings. Full paper PDF can be found at http://archive.bridgesmathart.org/2018/bridges2018-547.html
Abstract:
The Mandelbox is a recently discovered class of escape-time fractals which use a conditional combination of reflection, spherical inversion, scaling, and translation to transform points under iteration. In this paper we introduce a new extension to Mandelbox fractals which replaces spherical inversion with a more generalized shape inversion. We then explore how this technique can be used to generate new fractals in 2D, 3D, and 4D.