I first came across 'parquet deformations' many years ago in Douglas Hofstadter's wonderful book "MetaMagical Themas: Questing for the Essence of Mind and Pattern", 1986, Toronto: Bantam Books.
William Huff, a professor in architectural design at the State University of New York at Buffalo, invented the concept and technique of 'parquet deformations', apparently inspired in the 1960's by the famous "Day and Night" woodcut of Dutch artist Escher.
A parquet deformation is a mixture of a transformation and a distortion applied to a regular tessellation. The deformations are not arbitrary, but more or less satisfy two basic requirements:
(1) There is change only in one dimension, so that one can progressively see how one tile gradually becomes another;
(2) At each stage, the unit cell of the pattern can be modified so that it can tile the infinite plane.
Instructions: In the parquet transformation below either drag points b or H to dynamically change the amount of deformation or click on the 'Animate Point' button for these parameters to change automatically.
Whirly-gig: A dynamic parquet deformation
Here are two more links to parquet transformations: "Parquet Transformation: An introduction" by David Bailey and "Metamorphoses and deformations" by Craig Kaplan. By googling you can also find many more links and examples of parquet deformations.
Created by Michael de Villiers, 22 September 2013; updated 6 April 2022 with WebSketchpad.