George Stiny

Introduction to Shape and Shape Grammars

The definitions pertaining to the shape grammar formalism are developed in detail. In this paper, we take a whirlwind tour through the shape grammar formalism, and the definitions and ideas on which it is based. The formal machinery for the algorithmic definition of languages of two- and three-dimensional spatial designs is thus established.

The Palladian Grammar

A parametric shape grammar that generates the ground plans of Palladios villas is developed as a definition of the Palladian style. The grammar is applied to generate the plan for the Villa Malcontenta.

Ice-Ray: A Note on the Generation of Chinese Lattice Designs

The conventions used to construct traditional Chinese ice-ray lattice designs are investigated. Parametric shape grammars are defined for the recursive generation of these patterns.

Kindergarten Grammars: Designing with Froebel's Building Gifts

A constructive approach to the definition of languages of designs is outlined. Froebels building gifts are used to illustrate the approach.

The algebras of design

Shapes made up either of points, lines, planes, or solids belong to algebras that separately and in Cartesian products provide the main objects and devices used in shape grammars.

A Note on the Description of Designs

Shape grammars elucidate the composition of designs and at the same time provide the basis for the description of these designs in other terms.

The Grammar of Paradise: On the Generation of Mughul Gardens

The conventions used to design Mughul gardens are characterized. These conventions are represented by a parametric shape grammar.

Production systems and grammars: a uniform characterization

The common structure underlying production system formalisms is developed. A variety of production system formalisms are summarized in terms of this structure. The structure is useful both for understanding existing types of production systems and for developing new ones.

Shape Rules: Closure, Continuity, and Emergence

Topologies obtained via closure operations structure shapes according to computations in a shape grammar, so that emergence is compatible with continuity.

Two Exercises in Formal Composition

Spatial relations and shape grammars are defined. A spatial relation is specified by a finite number of shapes arranged in a certain way. A shape grammar provides for the recursive generation of arrangements of shapes in terms of given spatial relations. The possible spatial relations between two edge-connected polygons are characterised. The use of these spatial relations to define shape grammars generating distinct languages of shapes is discussed. The construction of shape grammars to generate infinite languages of shapes containing a given shape made up of polygons is also considered.