A Mathematical Formalization of Making Grammars

Kamath, Ayodh Vasant (2023) A Mathematical Formalization of Making Grammars. Nexus Network Journal. ISSN 1522-4600 (In Press)

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Making grammars model makers as perceiving their environment and acting to transform it. Shape grammars, which model designers as manipulating shapes, are then a special case of making grammars where perceiving is limited to seeing and doing is limited to drawing. This paper develops set-theoretical and graph-theoretical formalizations of making grammars. Existing set-theoretical formalizations of shape grammars show that designing is visual computing by demonstrating that a shape grammar can be devised to simulate any Turing machine. However, there are no mathematical arguments showing how making grammars describe computation. Using a previously published example of a shape grammar and its corresponding making grammar, this paper combines ideas from ecological psychology with methods from set theory and graph theory to show that, for each Turing machine, a making grammar can be devised which simulates it.

Item Type: Article
Keywords: Making Grammar | Shape Grammar | Material Computation | Design Theory
Subjects: Physical, Life and Health Sciences > Arts and Architecture
Physical, Life and Health Sciences > Engineering and Technology
JGU School/Centre: Jindal School of Art & Architecture
Depositing User: Amees Mohammad
Date Deposited: 05 May 2023 05:57
Last Modified: 05 May 2023 05:57
Official URL: https://doi.org/10.1007/s00004-023-00731-2
URI: https://pure.jgu.edu.in/id/eprint/5946


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