A Shape Modulus for Fractal Geometry Generation

Schor, Alexa L.; Kim, Theodore

A Shape Modulus for Fractal Geometry Generation

Files

v42i5_09_14905.pdf (191.96 MB)

paper1030_mm1.mp4 (201.69 MB)

Date

2023

Authors

Schor, Alexa L.
Kim, Theodore

Publisher

The Eurographics Association and John Wiley & Sons Ltd.

Abstract

We present an efficient new method for computing Mandelbrot-like fractals (Julia sets) that approximate a user-defined shape. Our algorithm is orders of magnitude faster than previous methods, as it entirely sidesteps the need for a time-consuming numerical optimization. It is also more robust, succeeding on shapes where previous approaches failed. The key to our approach is a versor-modulus analysis of fractals that allows us to formulate a novel shape modulus function that directly controls the broad shape of a Julia set, while keeping fine-grained fractal details intact. Our formulation contains flexible artistic controls that allow users to seamlessly add fractal detail to desired spatial regions, while transitioning back to the original shape in others. No previous approach allows Mandelbrot-like details to be ''painted'' onto meshes.

CCS Concepts: Computing methodologies -> Computer graphics; Shape modeling

        @article{10.1111:cgf.14905
,
journal = {Computer Graphics Forum},
title = {{A Shape Modulus for Fractal Geometry Generation
}},
author = {Schor, Alexa L. and 
Kim, Theodore
},
year = {2023
},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.
},
ISSN = {1467-8659
},
DOI = {10.1111/cgf.14905
}
}