Unitary Generative Design, a Quantum Formulation of Stiny's Shape Grammars

Shape grammars provide a formal account of generative design in which rules act directly on spatial configurations rather than on symbolic strings. Quantum computation, in parallel, has developed mature rewriting traditions for circuits and string diagrams, where equivalence is witnessed by rule-based transformations. This paper gives a unitary formulation of spatial shape rewriting. Designs are modelled as quantum states over a configuration basis of embedded geometries, and shape rules are modelled as unitary operators that implement reversible replacement on matched subspaces. The framework separates matching from application by introducing a coherent match register, and it recovers classical derivations as a coarse grained limit. Two quantum specific phenomena then become available for generative design, interference controlled emergence in which an emergent subshape can be amplified or suppressed by phase, and entangled subdesign constraints in which distant regions exhibit correlated stylistic outcomes without explicit classical coordination. The interference signature is operationally visible when match or history information is not resolved by the readout, or is coherently erased before feature measurement. The result is a mathematically explicit bridge between visual calculation in design and operator-based evolution in quantum theory, together with a route to simulation and empirical evaluation via feature observables and distributional tests.