For nearly four decades, the shape grammar discourse has described a different paradigm of design computing with the promise of revolutionizing computer-aided design (CAD). Its foregrounding of visual rules (shape rules drawn in a 2D or 3D modeling system) over symbolic rules (instructions defined in some programming language) has provided a robust theory for designers to believe in but nevertheless a formidable challenge to implement despite the best efforts of research groups at various schools and research labs all over the world. Among the 70+ shape grammar interpreters that have been designed since the seventies two of the most recent ones have originated in doctorate work in the Shape Computation Lab. These general interpreters include the GRAPE that implements a graph theoretic modeling of shape, and more recently, the Shape Machine, a software engine implemented in Python as a plug-in within Rhinoceros 6. Significantly, the Shape Machine features an unprecedented support of maximal line representation, subshape recognition and modification for straight lines and arcs under Euclidean transformations, and a visual interface that allows programming of custom functions by drawing shapes instead of writing code in a programming language thus offering a novel framework for the computations envisioned by the academic community and CAD users since the early seventies.

__ Shape Machine

__ DrawScript

__ Grape

Shape grammars provide one of the most powerful systems for the generative description of designs (Stiny, Knight, Earl, Krishnamurti, Flemming, more). Their unique difference with all other current generative systems is that they perform entirely visual computations rather than symbolic computations. Shape grammars are indeed intended to form a basis for purely visual computation, and in this sense, they belong in the heart of design education and practice – both in precedent analysis and in a studio setting. The projects presented below operate on a variety of scales including various domains, ambitions and means - including analog representations and operations executed by pencil and eraser or rule-bound play with Froebel blocks to database-supported hierarchies to mediated visual scripts in DrawScript mode in Shape Machine.

__ Palladio Computatus

__ Portm-Ino Automated

__ The Atrium Hotel Grammar

__ The Dirksen Variations

__ Mughal Gardens Redreamed

__ Terragni’s Riddle

__ Entelechy I

__ Kindergarten Courts

__ Courtroom Grammar

__ White Geometries

Mathematical models are routinely used in the description, interpretation and evaluation of architectural, spatial or sonic design. Here a range of tools from discrete math including theories of means, Pythagorean arithmetic, figurative numbers, symmetry, set theory, group theory, graph theory, lattice theory, matroids, permutations, combinatorics and Polya's theorem of enumeration are deployed to produce classes of shapes or notational systems that range from simple elements or fragments of visual and sonic thought such as grids, diagrams, notes and chords, all the way to complex configurational systems or aesthetic languages of designs that capture actual and/or possible design worlds. The list of the research projects given below is primarily concerned with the study of minimal geometric worlds to provide insight to expressiveness, possibilities - and for that matter - impossibilities in the setting of a design inquiry.

__ Shape Signature

__ Threeness

__ Ice-ray Tilings

__ n-Dipyramids

__ Sieves

__ Symmetry Lattices

__ Soundshapes

__ Rod Symmetry

__ Frit

__ Isovox

__ Hermes

__ Innercube

__ Cube Orbits

__ Four Eights

Designs emerge among the interrelations of symbolic descriptions including drawings, models, diagrams, renderings, texts, numbers and other symbolic data. Among them, the visual properties of the 2D and 3D geometric models – plans, sections, elevations, axons, perspectives, exploded axons and so forth, at all scales, views and combinations, and their different functionality in design workflows, including figure-ground diagrams, circulation diagrams, adjacency diagrams, visibility diagrams, lighting diagrams and so forth, provide an inexhaustible canvas for formal studies in the analysis of artifacts at all scales, from the object, to the urban frame. ShapePedia is a playful name for visually-driven, custom-made computer-aided tools designed and implemented in-house to foreground the formal description, interpretation and evaluation of given sets of designs.

__ Courtsweb III

__ Courtsweb II

__ Courtsweb I