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A symmetry-group semantics for shape grammars : lattice methods for the classification of strand-based patterns

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A symmetry-group semantics for shape grammars : lattice methods for the classification of strand-based patterns

Hortop, Eric (2007) A symmetry-group semantics for shape grammars : lattice methods for the classification of strand-based patterns. Masters thesis, Concordia University.

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Abstract

In ascribing information to designs, two of the purposes a researcher could have in mind are to classy designs, grouping them with similar designs and highlighting specific characteristics, and to store information for reproducing them. The notations and methods for these two tasks are likely to be different. In the Generative Design Project, researchers have undertaken classification of two-dimensional repeating patterns using symmetry groups, and storage for reproduction using a restricted form of shape grammars. This thesis demonstrates an approach to ascribing symmetry groups to shape grammars, allowing a researcher to concentrate their efforts on representing an artefact or collection, while retaining the benefits of a standard classification. This work defines a class of strand-based repeating patterns to which this approach is suited, outlines shape grammars in general and in a restricted context-free form, It also defines the symmetry information which is the output of the process starting with broad categories of isometric groups and working down to the information required to fully describe the symmetries of interest. The thesis also provides set, scalar and vector lattices used in the approach, and provides a novel, consistent method for carrying out the assignment of groups to grammars using those lattices and additional tests to bound the symmetries possible in the language of a given grammar conforming to the restrictions discussed. By establishing a symmetry-group semantics for shape grammars, this thesis allows a pattern or family of patterns to be more fully described by its shape grammar without requiring separate rendering and classification work

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Hortop, Eric
Pagination:xi, 77 leaves : ill. ; 29 cm.
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:2007
Thesis Supervisor(s):Szabo, Fred
ID Code:975475
Deposited By: Concordia University Library
Deposited On:22 Jan 2013 16:08
Last Modified:18 Jan 2018 17:40
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