ARC 4303A | 3, Shape grammar

Languages of designs can be defined by shape grammars, which have three important characteristics:
1. They are formal (transparent): they mean the same thing to everyone.
2. They are generative (productive): they produce new designs.
3. They are graphic (and symbolic).
This means that we have a graphic way of satisfying our three demonstrations of understanding.

How to use shape grammars

For an informal explanation, see Li (forthcoming, 3–4). For full technical details, see Stiny (1980).
Example: square grammar.
Example: line grammar.
To apply a shape rule:
- Compare the left shape with the current shape. If there is a match,
- Subtract (erase) the left shape from the current shape; and
- Add (draw in) the right shape. The resulting shape is the new current shape.
To be more precise:
- Compare the left shape under one or more Euclidean transformations (reflection, rotation, scaling, translation). If there is a match, then
- Subtract the left shape under the same transformation, and
- Add the right shape under the same transformation.
- We can express the process precisely like this:
- where
  - A is the left shape.
  - B is the right shape.
  - C is the current shape.
  - C′ is the new current shape.
  - t is one of the Euclidean transformations or a finite sequence thereof. (Notice that t appears three times, unchanged.)
  - – means subtract or erase.
  - + means add or draw.
  - ≤ means is a part of. There is a precise definition of part, but it’s a bit complicated. Think of it like this: if you put C on top of t(A), it will cover t(A) completely.
  - := means is assigned the value of.
This has two implications:
- If there is more than one transformation under which the left shape matches the current shape, then there is more than one way to apply the rule.
- There is no ambiguity about whether a rule can be applied or not. It does not depend on the user.

Automated grammar for ting tang sections

Download here:
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Assignment 3 out

Choose one of the example grammars. Call it grammar A.
Create grammar B by adding one rule to grammar A. Show:
- Grammar B;
- One design that is illegal in grammar A and legal in grammar B;
- One design that is legal in grammar A and illegal in grammar B; and
- One design that is legal in both grammars A and B.
Create grammar C by deleting one rule from grammar A. Show:
- Grammar C;
- One design that is illegal in grammar A and legal in grammar C;
- One design that is legal in grammar A and illegal in grammar C; and
- One design that is legal in both grammars A and C.
Create grammar D by changing one rule in grammar A. Show:
- Grammar D;
- One design that is illegal in grammar A and legal in grammar D;
- One design that is legal in grammar A and illegal in grammar D; and
- One design that is legal in both grammars A and D.
It may help to arrange these designs in a matrix.

Samples of student writing

No serious structural and spatial problem can be found in any of these legal designs.
z 柱: how many rafts the design have.
Since all the legal designs has a legal description accordingly, which is easier to be analyzed, generalized, and summarized to find same factors in common. One may put emphasis on the common words of description rather than the similar images of the picture.
They are legal because i have follow the instruction and use mathematical calculation together with the computer to draw these mesuare drawings.
For the roof section, all the legal design must be concave in shape in both side.
It is much more easier to do the task of designing illegal building section. It is because i always having a design that i could not named and therefore i should be said to a illegal design.
The observed construction pattern for this five cases seems to agree to that of the existing legal design.
The ‘juzhe’ system provide a formula which enable us to find out any legal design contained in the set.
It is legal becasue it is structurally stable and it satisfy all the assumptions.
The design is legal because it suits my assumptions that the longest beam stetch no longer than 6 rafters’ distance.
Secondly, the roof must be symmetry by the middle.
One rafter-beam only be allowed at the outest bays.
Otherwise, what a person “thinks” it is legal or not will be meaningless to anyone.
There is x rafts between the outest column and the column next to it.
as far as I am concerned , whether a design legal or not is not only defined by dead measure or architectural law, but only defined by building material ,(if 20 rafts length has overpass the limit of the material of wood , then the assumption of legal building with 20 rafts is actually legal only in a weird world. ) and many other reason such as history event, culture … perhaps my viewpoint may disappoint those people have a logic perspective; however, I insist that only by viewing from proper way, those legal designs have their real significance.

List of references

Li, Andrew I-kang. Forthcoming. The Yingzao fashi in the information age. Paper read at The Beaux-Arts, Paul-Philippe Cret, and 20th-century architecture in China, at University of Pennsylvania. Download text and images (PDF, 254 and 241 KB).

Stiny, George. 1980. Introduction to shape and shape grammars. Environment and planning B: planning & design 7: 343–351.