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[RA+88]  Computer Generation of Penrose Tilings

Rangel-Mondragon:1988:CGP (Article)
Author(s)Rangel-Mondragon J. and Abas A.S.
Title« Computer Generation of Penrose Tilings »
JournalComputer Graphics Forum
Volume7
Number1
Page(s)29--37
Year1988
URLhttp://www.eg.org/EG/CGF/volume7/issue1/v07i1pp29-37_abstract.html

Abstract
Tiling patterns have been of interest to artists, craftsmen and geometers for thousands of years. More recently, because of their applications in crystallography, in the machine shop for cutting and shaping of materials and in pattern recognition, they have also become of importance to chemists, physicists, engineers and workers in the field of Artificial Intelligence. Another reason for recent heightening of interest in the subject comes from the discovery in 1984 at the National Bureau of Standards in USA1 of a material whose diffraction pattern exhibits five-fold symmetry incompatible with a three dimensional space lattice. Such materials have since been called quasicrystals and it appears that their structure characterises an intermediate state between the structures of crystalline and amorphous substances. This discovery has the profoundest implications for material science. The theoretical explanation of the structure of quasicrystals has been given in terms of the mathematical theory of Penrose tiling2 Penrose tiles not only explain the order underlying quasicrystals but have mathematical properties of great interest.3 They also offer a new spatial structure for creating aesthetically pleasing designs in applied arts and because they generate packed structures with five-fold symmetries, the tilings may turn out to be useful in modelling of biological forms. Tiling theory comprises a vast body of knowledge which rather surprisingly has only very recently been brought together in a definitive treatise.3 Despite the explosive interest in the subject and the widespread references to Penrose patterns in the literature, only one early paper has appeared on their computer generation†. The object of our article is to describe Penrose tilings and develop an efficient algorithm for their generation. We will also give some examples of designs based on their structure.

BibTeX code
@article{Rangel-Mondragon:1988:CGP,
  optpostscript = {},
  number = {1},
  author = {Jaime Rangel-Mondragon and Abas, Amer Shaker},
  optkey = {},
  optannote = {},
  url = {http://www.eg.org/EG/CGF/volume7/issue1/v07i1pp29-37_abstract.html},
  localfile = {papers/Rangel-Mondragon.1988.CGP.pdf},
  optkeywords = {},
  journal = j-CGF,
  optmonth = {},
  optciteseer = {},
  volume = {7},
  optdoi = {},
  optwww = {},
  title = {{C}omputer {G}eneration of {P}enrose {T}ilings},
  abstract = {Tiling patterns have been of interest to artists, craftsmen and
              geometers for thousands of years. More recently, because of their
              applications in crystallography, in the machine shop for cutting
              and shaping of materials and in pattern recognition, they have
              also become of importance to chemists, physicists, engineers and
              workers in the field of Artificial Intelligence. Another reason
              for recent heightening of interest in the subject comes from the
              discovery in 1984 at the National Bureau of Standards in USA1 of a
              material whose diffraction pattern exhibits five-fold symmetry
              incompatible with a three dimensional space lattice. Such
              materials have since been called quasicrystals and it appears that
              their structure characterises an intermediate state between the
              structures of crystalline and amorphous substances. This discovery
              has the profoundest implications for material science. The
              theoretical explanation of the structure of quasicrystals has been
              given in terms of the mathematical theory of Penrose tiling2
              Penrose tiles not only explain the order underlying quasicrystals
              but have mathematical properties of great interest.3 They also
              offer a new spatial structure for creating aesthetically pleasing
              designs in applied arts and because they generate packed
              structures with five-fold symmetries, the tilings may turn out to
              be useful in modelling of biological forms. Tiling theory
              comprises a vast body of knowledge which rather surprisingly has
              only very recently been brought together in a definitive
              treatise.3 Despite the explosive interest in the subject and the
              widespread references to Penrose patterns in the literature, only
              one early paper has appeared on their computer generation†. The
              object of our article is to describe Penrose tilings and develop
              an efficient algorithm for their generation. We will also give
              some examples of designs based on their structure.},
  pages = {29--37},
  year = {1988},
}

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