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Computer Graphics


Norton Starr

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This site shows three of my computer graphic designs and describes one of them. Almost all my work in this area was produced in 1972-1973, during a sabbatical taken at the Department of Combinatorics and Optimization of the University of Waterloo, Waterloo, Ontario, Canada.

A number of my pictures of functions of two variables appeared in various texts in mathematics and in computer science during the 1970ís, 1980ís and 1990ís.


click to enlargeThe spiral illustrated here is composed of eighteen symmetric networks, from the smallest, a triangle, to the largest, which is formed by 190 line segments. These networks are illustrations of complete graphs: A complete graph on  n  vertices consists of all possible connections (edges) among pairs of vertices, and is denoted Kn. Among n vertices there are n(n-1)/2 such possible edges. Thus the smallest network shown, the triangle, represents K3; the next smallest network, having 6 edges, represents K4; then comes K5 with 10 edges;  . . . ; up through K20 with 190 edges.

In 1972-73 I was studying graph theory, and decided it could be interesting to illustrate an array of basic graphs in a spiral design.  I chose to have the size of the networks increase as the number of vertices increases, in such a way that each network has the same apparent visual density. For the underlying curve I used an Archimedean spiral (http://en.wikipedia.org/wiki/Archimedean_spiral), and located the center of each network on this curve. I also imposed a slight gap between adjacent networks, rather than having them touch. Satisfying these requirements, together with some other more recondite constraints, involved a considerable amount of analysis and experimentation, almost all of it purely computational. During the design stage, there were no more than two or three trial drawings because in that era it was very time consuming to produce such pictures. In contrast, I carried out repeated numerical experimentation in order to obtain locations for the centers of the networks and radii for them which were likely to yield the image I had in mind. 

This design was drawn in 1973 by fountain pen on a Calcomp drum plotter, driven by an IBM 360/75 computer. The result was then photo-reversed and reduced by fifty percent before being lithographed in black ink on white paper. (This year it was reprinted in an improved version from the 1973 negative.) The computing and drawing were carried out at the University of Waterloo Computing Centre.  I am grateful to Amherst College for support during my sabbatical leave in 1972-73 and to the Department of Combinatorics & Optimization of the University of Waterloo for providing me with a visiting appointment that year.  Thanks also are due to the staff of the Computing Centre at Waterloo, who taught me to use their facilities.


  • Ex Machina – Frühe Computergrafik bis 1979, Wulf Herzogenrath & Barbara Nierhoff-Wielk, eds., Deutscher Kunstverlag, München, 2007, p. 465.
  • The Secret Guide to Computers, 10th through 30th editions, Russ Walter, 1981-2007.
  • Computers and Problem Solving, Richard J. Kitto, McGraw-Hill Ryerson Ltd., Toronto, 1989, p. 300.
  • Computergrafik-Galerie, Herbert W. Franke, DuMont Buchverlag, Köln, 1984, p. 133.
  • Introduction to Computer Data Processing with BASIC, Margaret S. Wu, Harcourt Brace Jovanovich, New York, 1980, p. 428.
  • Trigonometry for College Students, Karl J. Smith, Wadsworth, Belmont, CA, 1977. Cover design.
  • Artist and Computer, Ruth Leavitt, ed., Creative Computing Press, Morristown, NJ, 1976, p. 2.  (Out of print, but available at  http://www.atariarchives.org/artist/sec1.php.)
  • Forward Citations in Graph Theory, G. Berman, ed., Math. Faculty,  Univ. of Waterloo, Waterloo, Ontario, 1975.  Front cover design.
  • Technology Review, V. 76, no. 1 (Oct./Nov., 1973), p. 58.
  • Computers and Automation, V. 22, no. 8 (Aug., 1973), p.13. 11th Annual Computer Art Exposition.


  • Epsten Gallery, Overland Park, KS, May-June 2019
  • Ex Machina – Frühe Computergrafik bis 1979, Kunsthalle Bremen, June 17 – August 26, 2007.
    (In the permanent collection)
  • Henion Bakery Gallery, Amherst, MA, August 1995.
  • printmaking: at the speed of thought, The Print Club, Philadelphia, November-December, 1989.
  • Computer Art in Czechoslovakia and the World, Palace of Culture, Prague, April 11-16, 1989.
    (In connection with Computer Graphics ‘89)
  • Sixth New Zealand Computer Conference, Auckland, July 1978.  (Third Prize, Static Class)
  • Art and the Computer, Worcester Art Museum, April-May, 1978.
  • 1977 International Computer Arts Exhibition, Tokyo, October 1977.
  • ICCH 3, The Third International Conference on Computing in the Humanities, Waterloo, Ontario, August 1977.
  • ACM '76, The Association for Computing Machinery Annual Conference, Houston, October 1976.
  • National Prints and Drawings Exhibition, Warbeke Gallery, Mount Holyoke College, April 1976.
  • ACM '75, Minneapolis, October 1975.
  • Canadian Computer Show, Toronto, October 1975.
  • Third International Computer Art Festival, CUNY, New York City, June 1975.
  • PRINTOUT, Watson Gallery, Wheaton College, April 1975.
    (In the permanent collection)
  • Beauty in Science, Science in Art, Pennsylvania State University, July 1974. 

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