This paper develops set-theoretical and graph-theoretical formalizations of making grammars.
Author
Ayodh Vasant Kamath, Associate Professor, Jindal School of Art & Architecture, O.P. Jindal Global University, Sonipat, Haryana, India.
Summary
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.
Published in: Nexus Network Journal
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