Wolfram Library Archive

Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings

From Form to Content: Using Shape Grammars for Image Visualization

Xiu Wu Huang
Cheryl Kolak Dudek
Lydia Sharman
Fred Szabo
Journal / Anthology

Proceedings of the Ninth International Conference on Information Visualisation (IV'05)
Year: 2005
Volume: 00
Page range: 439-444

The idea of superimposing geometric grids on images to visualize their content is not new. Leonardo Da Vinci used it, D¨urer used it, and Descartes pioneered the use of geometric grids to describe geometric content with algebraic equations. Shape grammars take the algebraic analysis of images to a new dynamic level. They permit the visualization of images in terms of construction processes: generators and relations, in the language of algebra. In this paper, we discuss some of the creativity involved in the identification of initial objects and rules for the analysis of both a Zillij mosaic and a Kuba cloth. We show that although conceptually similar, the processes are quite different for the two types of design. While Zillij mosaics are regular, Kuba cloths also involve scaling: the variation of the size of repeated sub-patterns within a defined space.

*Mathematics > Geometry > Plane Geometry
*Mathematics > Geometry > Tiling
*Mathematics > Recreational Mathematics