genomancer

I submitted a slightly modified version of my Bridges math/art conference paper from 2018 “Extending Mandelbox Fractals with Shape Inversions” to arXiv, and it’s now up at https://arxiv.org/abs/1809.01720

If anyone wants to cite this paper I currently prefer that they cite the arXiv version, since Google Scholar (and likely other publication indexing tools) has not yet indexed the version on the Bridges conference website.

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.

Images from experiments in replacing hypersphere inversion in 4D Mandelbox with hybrids of hypersphere and hypercube inversion.

Images from experiments in replacing spherical inversion in 3D Mandelbox with a cube shape inversion.