## Shape Grammars in Motion

###### Posted on 13 April 2013

How do we describe shapes that have kinetic properties that pivot, oscillate, or even slide? The variable m(x) meaning the motion of "x" tries to bring a shape grammar definition to this often overlooked component of design.

When working with shape grammars, the shape (usually defined by the variable “x”) can take the form of anything. Shapes can be two dimensional, three dimensional, planes, lines, or even points. The boundaries of these shapes allow us to classify their dimensionality from 0 to 3.  The entire enterprise of shape grammars can be described with three features: Shape Schemas, Shape Rules, and Shape Grammars.

Shape Schemas are the algebraic definition of the desired move or action operated upon a given shape. Shape rules are the graphic definition of the desired move or action. Shape rules always include an arrow of operation signifying that whatever is on the left hand of the arrow is computed into the right hand side of the arrow. Finally we have Shape Grammars that are a set of specific Shape Rules. This set of rules are the procedural steps of the rules carried out that yield the results of a design belonging to a design language of that give grammar.

#### x → x + m(x)

Stiny’s schemas accounts for every shape rule necessary to carry out basic design moves, but he makes the point that this is only an initial set of rules necessary to begin designing. Rules can be created or discarded at any time to meet the needs of the designer. This is what we call “flexible purposing.” In this spirit I tried to create a shape schema that could properly capture the notion of movement (m) embodied by a given shape. While the schema x → x + t(x) allows us to translate, rotate, reflect, or scale an object, it tells us nothing about the way in which the object physically moved. The schema x → x + m(x) along with the motion shape rules help designers describe shapes that have kinetic properties.

Quote: "Embedding lets me copy without copying by rote – there are no building blocks."
###### George Stiny

Shape grammars are all about visual calculation. Your eyes wander along a page or three dimensional composition and picks out what is important, what is relative, and what the designer wants to use. Through the eye lines and planes fuse together and separate just as easy, unlike the computer which constantly sees things and only interprets things as bits and units. When design elements are only perceived as 0 dimensional objects or as single discreet units this type of embedding cannot occur.

When we perceive shapes that have kinetic properties to them the same visual calculation is amplified by the number of frames or seconds the movement transpires. The above example shows a simple schema with a motion that happens in 80 frames. This is not to say that there are only 80 compositions that flicker before the eye. Each frame as a single composition has an array of embedded shapes and designs in it. Placing it in motion only lets the eye have more fun.

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