Automatic shape generation based on quadratic four-dimensional fractals

Authors:
Adam Goiński;Tomasz Zawadzki;Sławomir Nikiel
Affiliations:
Institute of Control & Computation Engineering, University of Zielona Góra, Zielona Góra, Poland;Institute of Control & Computation Engineering, University of Zielona Góra, Zielona Góra, Poland;Institute of Control & Computation Engineering, University of Zielona Góra, Zielona Góra, Poland
Venue:
ICCVG'12 Proceedings of the 2012 international conference on Computer Vision and Graphics
Year:
2012

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Abstract

Amorphous shapes have always been a challenge to CG modelers. Apparently natural in look, their topology is hard to retrieve manually. Scientists from different backgrounds have tried to understand and model such phenomena. Fractals belong to the most representative solutions, but still are rare in 3D domain. Methods for generation of fractal objects use mainly quaternion representations for nonlinear systems in four dimensions. In such a case advanced volumetric graphics methods need to be applied to convey multidimensional information. In the paper, we propose a simple and effective approach to use four-dimensional escape-time fractals as automated shape generator. We extend general quadratic fractal maps to four dimensions. The algorithm results in diverse aesthetically balanced volumetric shapes delivered in real time on a modern PC.