Asymmetry vs. Symmetry in a New Class of Space-Filling Curves

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Douglas M. McKenna: Asymmetry vs. Symmetry in a New Class of Space-Filling Curves. In: Bridges 2006. Pages 371–378



A novel Peano curve construction technique shows how the self-referential interplay between symmetry and asymmetry based on the translation, rotation, scaling, and mirroring of a single angled line segment that traverses a square evinces rich visual beauty and optical intrigue.

Extended Abstract


Used References

[1] H. Sagan, Space-Filling Curves, Springer-Verlag, ch. 1-3, 1994.

[2] D. M. McKenna, “SquaRecurves, E-Tours, Eddies, and Frenzies: Basic Families of Peano Curves on the Square Grid”, The Lighter Side of Mathematics: Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History, MAA, pp. 49-73, 1994.

[3] B. B. Mandelbrot, “Harnessing the Peano Monster Curves”, The Fractal Geometry of Nature, Freeman, pp. 68-69, 1982 (illustrated in part by the present author, see p. 444).

[4] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, pp. 12-14, 1990.


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