As such, the term parquet deformation, despite having connections to tessellation, may be wholly unfamiliar to most people (even including those with knowledge of tessellations), as is indeed the whole concept of such an idea. Such an aspect of tessellation has received scant coverage, and in my opinion disproportionately so as to its inherent worth. Therefore, to clarify such matters, I now define a parquet deformation as a geometrical tessellating metamorphosis, of which this is usually shown as a ‘long strip' (with typical examples in Parquet Deformation 1), although other formats are indeed possible (and shown in Parquet Deformation 2).

As such, in contrast to any ‘orthodox' picture, for example a portrait or landscape, this is not intended to be viewed en masse, but is instead intended to be ‘scanned' by the eye, and utilising the examples below, in a left to right or vice versa direction. Whereupon having so done, a given tiling thus can be seen to gradually metamorphosise in outline, until upon ‘completion' of its metamorphosis it is unrecognisable from its beginning.

Concerning the history and background to parquet deformation, only in relatively recent years has such an idea come to the fore. Indeed, despite tessellations per se having been of interest for centuries, such a apparently simple concept was apparently not thought. As such, to all intents and purposes, the originator of the idea is of William S. Huff, with examples dating back to the 1960s. Although earlier, isolated examples do indeed occur, such as in parts of Escher's Metamorphosis, and also some isolated examples ‘of sorts' in the book Pattern Design by Lewis Day, these cannot be considered equal in any way to Huff's more thorough and systematic work in this field, albeit he himself does not compose these in the sense of the word. Indeed, Huff has, in his role as Professor of Architecture at the State University at New York (SUNY) not only brought the concept of such a thing to the fore, but has also inspired numerous students of his to compose many new examples, many of notable skill and ingenuity. Such studies eventually led to the first popular account, with the publication (1983) of his students work in the Scientific American article ‘Parquet Deformations: Patterns of Tiles That Shift Gradually in One Dimension' by Douglas Hofstadter. Further examples by Huff's students are to be seen in Intersight One. However, despite these initial, promising beginnings, subsequent interest has been lukewarm, to say the least, with no books or papers appearing, at least to my knowledge. Indeed, it can be said the subject went into a slumber, and has only relatively recently been revived, at least in published form, with new examples in 1998, comparable in quality to the students of Huff's, most notably with examples by Craig S. Kaplan and John Sharp, details of which appear on the links page.

However, despite the above ‘revival', such as it is, somewhat disappointingly I still find so few people undertaking new examples or who are at least interested in this aspect of tessellation, and so I would be more than interested in hearing from fellow enthusiasts on this matter, especially from the ex-students of Huff's.

Last Updated: 29 September 2009