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Parquet Deformations of Craig Kaplan
Craig S. Kaplan (1972–), the Canadian computer scientist and mathematician whose work bridges mathematical art and computer graphics, can fairly be described as the leading figure in contemporary parquet‑deformation research. He brings a formidable mathematical sensibility to the subject and presents a wealth of innovative, technically sophisticated examples that would be virtually impossible to construct without computational assistance.
Parquet deformations are often shown in their most elementary form: a linear strip. This is perfectly serviceable—there is nothing inherently wrong with it—but it represents only a narrow slice of what is geometrically possible. Kaplan demonstrates how the idea can be expanded into far richer configurations. Building on the one‑dimensional strip, he explores fully two‑dimensional deformations in a square format, where the transformation becomes “continuous all over,” propagating left–right and top–bottom. He also shows how a deformation can be closed into a loop, producing circular variants.
Further innovations include parquet deformations based on Islamic tiling patterns. Because of the structural complexity of these tilings, such examples would be essentially unattainable by traditional hand methods; Kaplan’s computational approach makes them not only feasible but elegant. In a similar spirit, he extends the concept to fractal‑based deformations. He also investigates transitions between Laves tilings and examines families of isohedral tilings.
Some of the work draws on sophisticated algorithms developed by others—well beyond the reach of typical recreational mathematics—such as methods by Hans Pedersen and Karan Singh. The result is a remarkably rich and technically impressive body of work. Kaplan has also written extensively on the subject in a series of articles, all of which are essential reading and are made readily accessible.
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All images © Craig Kaplan, with permissions for non-commercial use.
Bibliography
Bellos, Alex. ‘Crazy paving: the twisted world of parquet deformations’. The Guardian, 9 September 2014
Essentially, a substantial feature of Craig Kaplan’s work, rather than a general discussion on the subject, as the title may otherwise indicate. Be that as it may, it is all mightily impressive and is of required reading. Of a cross-section of his work, in which he brings his full range of computer scientist/mathematical abilities to the premise, leaving lesser mortals far behind. Most of these are simply impractical without the aid of a computer. Bellos captions these as: Grid-based parquet deformation, Funky tiles, Iteration deformations, Organic labyrinth growth, Islamic tiling, 2D parquet deformation, and Circular deformation.
Unusually, these are shown coloured. Kaplan is one of the few who use colour, of both flat and graduated colours.
https://www.theguardian.com/artanddesign/alexs-adventures-in-numberland/2014/sep/09/crazy-pavin-the-twisted-world-of-parquet-deformations
Kaplan, Craig S. Computer Graphics and Geometric Ornamental Design. A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, University of Washington, 2002
A major writing, with 18 references to parquet deformation.
https://cs.uwaterloo.ca/~csk/other/phd/kaplan_diss_full_screen.pdf
————. ‘Islamic star patterns from polygons in contact’. Proceedings of Graphics Interface 2005, pp. 177–185
Nine mentions of parquet deformation within the context of an Islamic style.
https://pdfs.semanticscholar.org/2924/e3afe0a0c07bd1f02fbe1089dcb8b4516212.pdf
————. ‘Curve Evolution Schemes for Parquet Deformations’. In Bridges 2010 Mathematical Connections in Art, Music and Science, pp. 95–102
31 mentions of parquet deformation of a dedicated piece on the subject. Some most impressive, highly advanced (in concept) parquet deformations.
http://archive.bridgesmathart.org/2010/bridges2010-95.pdf
————. ‘Animated Isohedral Tilings’. Bridges 2019 Conference Proceedings, pp. 99–106
Four mentions of parquet deformation within the context of animated isohedral tilings.
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