Curving Spirolaterals

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Robert J. Krawczyk: Curving Spirolaterals. In: Bridges 2001. Pages 29–36



Spirolaterals are square spirals constructed of straight lines of increasing length. This paper investigates methods that can be used to transform their straight line turns into curves. From the tens of thousands of possible spiro laterals which have beell found, that are all closed, with and without reversed turns, a series of artworks is developed showing possible curving methods: curve jitting, splines, inversion, antiMercator and circular trallsforlllations, along with hypocycloid and epicycloid curves. These transformations are implemented using CAD methods and custom software. A series ofparameters are discussed which generate a variety of arn.llork.

Extended Abstract


Used References

[1] Abelson, Harold, diSessa, Andera, 1968, Turtle Geometry, MIT Press, pp.37-39, 120-122

[2] Dixon, Robert, 1987, Mathographics, Dover Publications, Inc., p.152

[3] Gardner, Martin, 1986, Knotted Doughnuts and Other Mathematical Entertainments, W. H. Freemand and Company, pp. 205-208

[4] Krawczyk, Robert, 1999, "Spirolaterals, Complexity from Simplicity", in International Society oj Arts, Mathematics and Architecture 1999, edited by N. Friedman and 1. Barrallo, The University of the Basque Country, pp. 293-299

[5] Krawczyk, Robert, 2000, "The Art of Spirolaterals", in The Millennial Open Symposium on the Arts and Interdisciplinary Computing, edited by D. Salesin and C. Sequin, University of Washington, pp. 127- 136

[6] Krawczyk, Robert, 2000, "The Art of Spirolateral Reversal", in International Society oj Arts, Mathematics and Architecture 2000, edited by N. Friedman, University of Albany-SUNY

[7] Lawrence, J. Dennis, 1972, A Catalog oJSpecial Curves, Dover Publications, Inc., p.43

[8] Odds, Frank, "Spirolaterals", Mathematics Teacher, February 1973, pp.121-124

[9] Weisstein, Eric, 1999, Concise Encyclopedia oj Mathematics, CD-ROM edition 1.0, Chapman & Hall/CRCnetBASE


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