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Spirolaterals Revisited

Last week, the notion of spirolaterals was introduced, providing students with explorations of associated number and geometric patterns. But, this is only the "tip" of the subject of spirolaterals.

To consider possible elaborations or extensions, consider the site Count On. It connects spirolaterals to the general idea of spirals, notes that they were invented by British biochemist Frank Olds in 1973, and then shows variations using "grid-warps," angle rotations other than 90 degrees, and anamorphic circular grids (shown on the right). The site also allows you to download/print various types of grid-warps.

Robert J. Krawczyk, Assistant Professor of Architecture at Illinois Institute of Technology, has pushed the idea of spirolaterals into the realm of art, with his website BitArt offering a fascinating gallery of examples. Be sure to watch the dynamic generation of his curved spirolaterals by clicking on "The Series" or playing with his Java applet.

In case you are interested, Professor Krawczyk also has written a great many "understandable" papers on the topic of spirolaterals. Rather than list the papers here, it is easier to refer you to his home page. While browsing through all of his papers, I encourage you to branch out and also look at his papers on "Technology and Art: A Kenetic Sculpture," "Mobius Connections in Architecture," "Architectural Forms by Abstracting Nature," and "Hilbert's Building Blocks." This guy is somebody I need to meet!