Shortly after shape grammars were invented by Stiny and Gips, a two part project for shape grammars was outlined by Stiny. In a 1976 paper Reference,Stiny described “two exercises in formal composition”. These simple exercises became the foundation for the many applications of shape grammars that followed, and suggested the potential of such applications in education and practice. The first exercise showed how shape grammars could be used in original composition, that is, the creation of new design languages or styles. The second exercise showed how shape grammars could be used to analyze known or existing design languages. Both exercises illustrated the unique characteristics of the shape grammar formalism that helped motivate almost a quarter century of shape grammar work. General but simple, formal yet intuitive: qualities that continue to make shape grammar disciples and confound skeptics.

Shape grammar theory and applications are well documented and represented in the literature on design computation and related areas. A shape grammar is a set of shape rules that apply in a step-by-step way to generate a set, or language, of designs. Shape grammars are both descriptive and generative. The rules of a shape grammar generate or compute designs, and the rules themselves are descriptions of the forms of the generated designs.

Shape grammars have properties aimed at making them especially suitable for designing, without sacrificing formal rigor. First, the components of shape rules are shapes: points, lines, planes, or volumes. Shape rules generate designs using the shape operations of addition and subtraction, and spatial transformations familiar to designers such as shifting, mirroring, and rotating. In short, shape grammars are spatial, rather than textual or symbolic, algorithms. Second, shape grammars treat shapes as nonatomic entities--they can be freely decomposed and recomposed at the discretion of the designer. This liberty allows for emergence--a feature that distinguishes shape grammars from set grammars, the most common kind of formal grammar. Emergence is the ability to recognize and, more importantly, to operate on shapes that are not predefined in a grammar but emerge, or are formed, from any parts of shapes generated through rule applications. Third, shape grammars are nondeterministic. The user of a shape grammar may have many choices of rules, and ways to apply them, in each step of a computation. As a design is computed, there may be multiple futures for it that respond differently to emergent properties, or to other conditions or goals.

To the right is a two-rule grammar that illustrates these properties. The first rule shifts a square halfway along a diagonal axis of the square. The second rule shifts an L-shape, also along a diagonal axis. Registration marks in each rule show the positions of the shapes on the left-side and right-side of the rule relative to each other. The starting shape for computations, called the initial shape, consists of two L-shapes. The two rules apply to this shape and to shapes produced from it by matching the square or L-shape on the left-side of either rule with a square or L-shape in a design. The square or L-shape in either rule may be translated, rotated, reflected, or scaled in order to match a shape in a design. If a match is made, the matched shape in the design is then replaced with a shifted shape as indicated in a rule. The direction of the shift depends on the spatial transformation used to make the match.

initial shape
derivation_animated_rule1.gif (1677 bytes)

Below is a computation of a design using the grammar. From the second step on, the rules can apply to either emergent L-shapes or emergent squares. Also from the second step on, either the first or the second rule can be applied to a design. The user of the grammar, human or machine, must decide which rule to apply and to which shape in a design to apply the rule.

click to see derivationsall1.gif (4691 bytes)a

Below is another computation using the grammar. The computation is identical to the one above in the first three steps. Then it diverges and follows a different path to produce a different design. Many other computations are possible with the grammar.

click to see derivationsall2.gif (4569 bytes)a

Shape grammar theory has advanced over the years to include complexities of shapes and shape computations beyond what is illustrated above. Parametric shape grammars Reference  compute designs with variable or parametric shapes. Color grammars Reference  and grammars with weights Reference  compute designs with shapes and properties of shapes (such as color, material and function). Description grammars Reference  compute descriptions of designs. Structure grammars Reference compute designs as structures or sets of shapes. Attributed grammars Reference compute designs with attributes and constraints on attributes. Parallel grammars or grammars defined in multiple algebras Reference  simultaneously compute different shape, text, or symbolic representations of designs (for example, plans, sections, and elevations together with verbal descriptions of them). All of these extensions to the original shape grammar formalism have been developed in order to compute certain kinds of designs more easily or expressively than with a standard shape grammar. However, none add to the computational power of a standard shape grammar which is equivalent to a Turing Machine, the most powerful computational device yet defined.

The history of shape grammar applications in architecture and the arts for the two complementary problems of original design and analysis is sketched in the first section of this paper. These two categories of applications do not have rigid boundaries, and are used mainly as a framework for discussion. An overview of the roles of shape grammar applications in education and practice is given in the second section. New and ongoing issues concerning shape grammars in education and practice are discussed in the last section.