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Lifelike Tessellations

By Andrew Crompton

Abstract

Although most people know of lifelike tessellations through the work of the Dutch artist M.C.Escher, (1898-1972) it often comes as a surprise to learn that he did not invent them and that they have their origins in Art Nouveau. Dense space filling designs can be seen in many patterns from this period, for example in the work of William Morris, several of whose fabrics patterns have closely packed leaves and flowers separated by a black line, with each leaf bending to fit its neighbour. This drawing by Nellie Syrett for the Yellow Book of 1896 is, if you like, a larval tessellation, insofar as a motif fills space and the background has vanished. It misses only because the motifs are read as overlapping rather than interlocking. It strikingly resembles the first tiling pattern which Escher drew, his “Eight Heads ” of 1922. The first true lifelike tiling, where figure and ground become one, was probably ‘Trout Dance ” by Koloman Moser in the Viennese magazine Ver Sacrum in 1901, (4). It would have remained a curiosity had it not been for Escher, who made the subject his own by producing about one hundred and fifty of them during his life. He used them as raw material for his geometrical fantasy drawings and raised the art of inventing interlocking shapes to new and preposterous heights, (1). Drawing them became something of a mania for him. Since his time very few new tessellations have been published. Interested readers can find an entertaining pornographic example in issue 44 of the underground magazine 'OZ ' (1972), and three more, using bees, flowers and fish were produced in 1976 by Marjorie Rice, a San Diego housewife who had first made her name by discovering four hitherto unknown types of pentagons which tile the plane. Her patterns, which are based on the pentagons, and her achievements as an amateur mathematician are described in the book 'The Mathematical Gardner'(2). figure

Year: 2009
OAI identifier: oai:CiteSeerX.psu:10.1.1.134.3550
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