Geometric Models of Composition Structures of National Crafts Patterns

Uzbek national crafts include a complex geometric system that has been formed over the centuries. This article presents a comparative analysis of four methodological approaches to the representation of the compositional structures of the three main families of patterns of this system — girih, islimiy and gul — in a digital environment — the theory of symmetry groups, parametric geometric modeling, shape grammar and L-systems. Symmetry groups are shown to be powerful in invariant pattern classification, while parametric modeling is powerful in flexible encoding of motif geometry. While shape grammar represents the pattern creation process as a system of rules, L-systems (Lindenmayer systems) open up new possibilities for algorithmic generation of fractal and botanical patterns through a recursive parallel rewriting mechanism. The proposed multi-layer integral geometric model N = ⟨G, Λ, F, S, P, R, T, Lₛys, Gᵣules⟩ combines these four approaches in a hierarchical manner and serves as a theoretical basis for digital archiving and algorithmic generation of national patterns.