Extending Mandelbox Fractals with Shape Inversions
Gregg Helt
TL;DR
This paper introduces a novel extension to Mandelbox fractals by replacing spherical inversion with shape inversion, enabling the creation of new fractals across multiple dimensions.
Contribution
It presents a generalized shape inversion method for Mandelbox fractals, expanding their diversity and dimensionality beyond previous spherical inversion techniques.
Findings
New fractals generated in 2D, 3D, and 4D
Enhanced diversity of Mandelbox structures
Potential for further exploration of shape-based fractals
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.
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Taxonomy
TopicsImage Retrieval and Classification Techniques