MATHS IS BEAUTIFUL

A ‘snowfake’ that is the product of an elaborate computer model designed to replicate the

complex growth of snow crystals. Created by mathematicians David Griffeath of the

University of Wisconsin-Madison and Janko Gravner from the University of

California, Davis, the model can generate all of nature’s snowflake

types in rich, 3D detail.

Images by Janko Gravner and David Griffeath

3D images of the limit set of a 4D Kleinian group.

Image by Jos Leys, www.josleys.com

Sierpiński triangle: a fractal that forms a geometric pattern

that can be reproduced at any magnification of reduction.

Named after Polish mathematician

Wacław Sierpiński.

46 INTERNATIONAL INNOVATION

IN PICTURES

Images by Dan Gries, www.dangries.com

Mandelbrot set: a set of complex numbers with convoluted fractal

boundary when plotted.

Left: based on the interference pattern of multiple waves emanating from the centre of the canvas, various mathematical methods are used to scale, clamp and smooth the wave patterns, and a gradient colour scheme is applied to map the wave values to colour.

Above: this image evolved from experiments in creating jagged, ‘noisy’ circles using a fractal subdivision method. A closed cylindrical object is defined by allowing a closed curve to sweep left-to-right across the canvas as it morphs from one of these noisy circles to the next. A cosine function is used for smooth interpolation during the morphing stages. The result is an object that marries jaggedness in one direction and smoothness in a perpendicular direction. The semi-transparent, gradient-coloured curves accumulate into this silky effect.

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