Algorithms for Morphing Escher-Like Tessellations

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Kevin Lee: Algorithms for Morphing Escher-Like Tessellations. In: Bridges 2015. Pages 483–486



Inspired by the way M.C. Escher combined metamorphosis and regular division in his art, I explore linear and non-linear algorithms that automatically morph tiles from the base polygon to a final shape. The morphing can be visualized as an animation or as a parquet deformation.. The final algorithm involves an interactive cubic spline, path-based editor that gives the artist fine control over the intermediate morph frames.

Extended Abstract


 author      = {Kevin Lee},
 title       = {Algorithms for Morphing Escher-Like Tessellations},
 pages       = {483--486},
 booktitle   = {Proceedings of Bridges 2015: Mathematics, Music, Art, Architecture, Culture},
 year        = {2015},
 editor      = {Kelly Delp, Craig S. Kaplan, Douglas McKenna and Reza Sarhangi},
 isbn        = {978-1-938664-15-1},
 issn        = {1099-6702},
 publisher   = {Tessellations Publishing},
 address     = {Phoenix, Arizona},
 note        = {Available online at \url{ }},
 url         = { },

Used References

[1] Bruce Bilney, Curly Elephants Tessellations, (as of April 20, 2015)

[2] Craig S. Kaplan. Curve Evolutions Schemes for Parquet Deformations. In Bridges 2010: Mathematical Connections in Art, Music and Science, pages 95-102, 2010.

[3] Craig S. Kaplan. Metamorphosis in Escher’s art. In Bridges 2008: Mathematical Connections in Art, Music and Science, pages 39–46, 2008.

[4] Doris Schattschneider. M.C. Escher: Visions of Symmetry. Harry N. Abrams, second edition, 2004.

[5] Kevin D. Lee. Tile Types in TesselManiac,, (as of April 20, 2015)

[6] Kevin D. Lee TesselManiac! 2014 (as of April 20, 2015)

[7] Thomas W. Sederberg, Peisheng Gao, Guojin Wang, and Hong Mu. 2D shape blending: An intrinsic solution to the vertex path problem. In James T. Kajiya, editor, Computer Graphics (SIGGRAPH ’93 Proceedings), volume 27, pages 15–18, Aug 1993


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