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 three of the most recent ones have originated in the Shape Computation Lab. These general interpreters include the GRAPE that implements a graph theoretic modeling of shape, the Shape Machine, an engine implemented in Python as a plug-in within Rhinoceros 6, and more recently, the Shape Machine 1.0 for Rhino 8, a shape grammar interpreter written from scratch in an object-oriented architecture. Significantly, Shape Machine features an unprecedented support of maximal line representation, subshape recognition and modification for points, lines and arcs under Euclidean and affine transformations, and a visual interface that allows programming of custom functions by drawing shapes instead of writing code in a programming language.

Why haven’t the Find and Replace operations, so essential in Word and Excel, been implemented yet in CAD? What would happen if we could seamlessly use vector-based shape rewrite-based operations with CAD operators in a logical processing framework to literally write programming code by drawing shapes? How would this affect our current view of computation, and what would it mean for design? Shape Machine is a new computational technology developed at the Shape Computation Lab at Georgia Institute of Technology that takes on heads on these questions by fundamentally redefining the way shapes are represented, indexed, queried and operated upon. Shape Machine's foregrounding of visual rules (shape rules drawn in a 2D or 3D modeling system) over symbolic rules (instructions defined in some programming language) provides a robust technology for engineers, computer scientists, designers, students and educators, and in general academics and professionals who use drawings and visual models to develop and communicate their ideas.

Shape grammars provide one of the most powerful systems for the generative description of designs. 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.

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.

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 geometric models including figure-ground diagrams, circulation diagrams, adjacency diagrams, visibility diagrams, lighting diagrams, at all scales, views and combinations and embeddings in 3D models, provide an inexhaustible canvas for formal studies in the analysis of artifacts at all scales, from the artifact to its urban context.

The first symposium on the unveiling of Shape Machine back on April 11, 2019, presenting the first version of Shape Machine, a new computational, visual and disruptive CAD technology developed at the Shape Computation Lab at Georgia Institute of Technology, to leading experts in various fields including AI,architecture, design, engineering, computer science, mathematics and other fields.