Design of Alphabets with Fourier Transforms

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Two-dimensional Fourier transforms give a description of pictures with local frequencies in the form of an array. A second transformation leads back to the original picture. A small arbitrary change in the frequencies of the first transformation's array produces a picture similar to the original picture but with aberrations of ornamental character.

Contributed by: Herbert W. Franke (March 2011)
Open content licensed under CC BY-NC-SA



After selecting the letter, you can use the parameters "radius" and "extension" to select various types of stencils to vary the ornamental letter style—an array in black and white shows the selected stencil. With "color set" you can select the color palette, and you can also use the parameter "color shift" for the cyclic exchange of the order of colors for an optimal aesthetic impression.

This is the last contribution of three for the Wolfram Demonstrations Project based on collaboration with my friend Horst Helbig, who died in the autumn of 2007; it is dedicated to his memory. See also the Demonstrations in the Related Links.


H. W. Franke and H. S. Helbig, Die Welt der Mathematik - Computergrafik zwischen Wissenschaft und Kunst", Düsseldorf: VDI-Verlag, 1988.

H. W. Franke and H.S. Helbig, Generative Mathematics: Mathematically Described and Calculated Visual Art, in Michele Emmer (ed.), The Visual Art, Cambridge, London: The MIT Press, 1993.

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