Factor Group Transformations on Escher Patterns

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Joshua Jacobs: Factor Group Transformations on Escher Patterns. In: Bridges 2005. Pages 457–462



The artist M.C. Escher intuitively expressed many mathematical concepts in his graphic designs. One of these concepts was that of transformations between different factor groups over the complex plane. We describe a method whereby any tiling that can be expressed as a rectangle system can be mapped to a multiplicative factor group over the complex plane.

Extended Abstract


Used References

[1] B. de Smit and H.W. Lenstra, The Mathematical Structure of Escher's Print Gallery, Notices of the AMS, April 2003, pp 446-451.

[2] escherdroste.math.leidenuniv.nl, Escher and the Droste Effect, Leiden University, Leiden, The Netherlands

[3] Doris Schattschneider, Visions of Symmetry, W.H. Freeman, 1990.

[4] Bruno Ernst, De toverspiegel van M.C. Eshcer, Meulenhoff, Amsterdam, 1976; English translation by John E. Brigham: The Magic Mirror of M.C. Escher, Ballantine Books, New York, 1976.

[5] E. Thé (design), The Magic of M.C. Escher, Harry N. Abrams, New York and London, 2000.


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