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university of calgary, canada,
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Computer Generated Celtic Knotwork using L-system Graphics,
Dave Carroll and Mike Scott.
In any domain where objects are sufficiently regular there may be an opportunity to develop a grammar based model of their geometric structure. One such domain is Celtic knot work particularly knot work of the type found in Celtic manuscripts such as the Book of Kells. Modelling such knot work using a grammar based approach based on L-systems is the subject of this paper. The paper describes the addition of a curve drawing construct to L-systems to allow the encoding of curved figures. A construct is developed which enables Bezier curves to be drawn using L-systems. This construct is used to model Celtic knot patterns. The patterns are encoded in an L-system and used as meta-patterns to construct simple carpet-pages made up of multiple knot patterns. A prototype production rule system and graphics interpreter for L-system strings using turtle graphics is also described. The problem of under-crossing and over-crossing of knot cords is addressed using Z-axis perturbation. This enables the generation of self-avoiding curves in three-space to give realistic looking knot patterns in 3D.
A book, not online: Hans Sagan, Space-Filling Curves, Springer-Verlag, New York, 1994. ISBN: 0-387-94265-3.
GEOMETERS (& OTHER GREATS) I SHOOK HANDS WITH
MOHAMED ALY (THE BOXER)
IVERSON ( THE INVENTOR OF apL )
BENOIT MANDELBROT
WOLFRAM (A NEW KIND OF SCIENCE AND MATHEMATICA)
COXETER
COXETER IN ENCYCLOPEDIA BRITANNICA
Coxeter, H(arold) S(cott) M(acDonald)
British-born Canadian geometer
(b. Feb. 9, 1907, London, Eng.?. March 31, 2003, Toronto, Ont.),
was a leader in the understanding of
non-Euclidean geometries,
reflection patterns,
and polytopes (higher-dimensional analogs of three-dimensional polyhedra).
His work served as an inspiration for R. Buckminster Fuller's concept of
the geodesic dome and, particularly, for the intricate geometric·
Coxeter, H S M... (75 of 176 words)
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FASS (space-filling, self-avoiding, simple and self-similar) curves
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AFFINE TRANSFORMS
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ANCIENT SYMBOLS
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DRAWING
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