The Art of Random Fractals

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Douglas Dunham and John Shier: The Art of Random Fractals. In: Bridges 2014. Pages 79–86



We describe a mathematically based algorithm that can fill a spatial region with an infinite sequence of randomly placed and progressively smaller shapes, which may be transformed copies of one motif or several motifs. This flexible algorithm can be used to produce a variety of aesthetically pleasing fractal patterns, of which we show a number of examples.

Extended Abstract


Used References

[1] Paul Bourke web site: colour/randomtile/ (accessed May 3, 2014)

[2] Benoit Mandelbrot Fractals: Form, Chance and Dimension, W.H. Freeman and Company, San Francisco, 1977.

[3] John Shier, Filling Space with Random Fractal Non-Overlapping Simple Shapes ISAMA 2011 Conference Proceedings, page 131, June 13–17, 2011.

[4] John Shier and Paul Bourke, An Algorithm for Random Fractal Filling of Space, Computer Graphics Forum, Vol. 32, Issue 8, pp. 89-97, December 2013. Also available on Shier’s web site: (accessed May 3, 2014)

[5] John Shier web site: geom linkpage.html (accessed May 3, 2014)


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