Craig Kaplan

Parquet Deformations of Craig Kaplan

Craig S. Kaplan (1972–), a Canadian computer scientist/mathematician, with an interest in mathematical art and computer graphics, can quite simply be described as the leading light in parquet deformation research. In short, he brings his superior mathematical mind to bear on the topic and shows a whole host of innovative and advanced examples that without the aid of the computer would simply otherwise be impractical. Typically, parquet deformations are portrayed in a ‘simple’ manner, as a linear strip. However, although all well and good (and there is nothing ‘wrong’ with this), other geometric configurations are indeed possible, in which the concept is expanded, and so is thus made arguably more interesting. For instance, as shown by Kaplan below, building upon the one dimension, two dimensions are possible, with a squared format, in which the deformation is ‘continuous allover’; left/right, top/bottom. Another variation they can be turned into a loop, with a circle. And another innovation is that of an Islamic tiling theme, where, due to the somewhat involved nature of the tiling these are shown possible that simply would otherwise be impractical by traditional hand methods. And again, of a similar involved vein in concept, fractals are also shown. The transitions between the Laves tilings are also investigated, as is a study of the isohedral tilings. In addition, there are also complex computer algorithms developed by others applied here (way beyond the typical recreational mathematical knowledge to compile such ‘simple’ linear instances), such as that by Hans Pedersen and Karan Singh. All of which embodies a most impressive body of work. Further, he has written extensively on the subject with a variety of articles, below, all of which all can be considered as must reading (and pleasingly has made these readily accessible).

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All images © Craig Kaplan, with permissions for non-commercial use.


Bellos, Alex. ‘Crazy paving: the twisted world of parquet deformations’. The Guardian, 9 September 2014
Essentially a substantial feature on 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.

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, of 18 references to parquet deformation.

————. ‘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.

 ————. ‘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.

————. ‘Animated Isohedral Tilings’. Bridges 2019 Conference Proceedings, pp. 99–106

Four mentions of parquet deformation within the context of animated isohedral tilings.

Page created 18 February 2021.