1. Introduction to shape grammars
Professor Terry Knight, MIT
MIT/Miyagi Workshop: Assignment 1
February 7-12, 2000

2. ASSIGNMENT
On the following pages you are asked to look at
three different ways of working with a shape grammar:
1. Using a shape grammar
Following rules
Finding a derivation of a design
2. Changing a shape grammar
3. Discovering a shape grammar

3. 1a. Using a shape grammar Following rules
On the next page, a 3 rule shape grammar is shown.
The first two rules add a shape to an existing shape.
The third rule erases a label.
Beginning with the initial shape, apply the first two rules
alternately to generate a design. Finish the derivation by
applying the third rule to erase a label.

4. SHAPE GRAMMAR
initial shape
rules

5. Finding a derivation of a design
1b. Using a shape grammar
Finding a derivation of a design
On the next page, a 1 rule shape grammar is shown.
The rule overlaps a square onto an existing square.
A design generated by the rule is also shown.
Show a step-by-step derivation of the design using the rule.
Each step represents one rule application.

6. 
rule
SHAPE GRAMMAR
initial shape
DESIGN

7. 2. Changing a shape grammar
Below is Frank Lloyd Wright’s plan for St.Mark’s-in-the-Bouwerie
apartment building (1929).

8. The St. Mark’s plan became the basic compositional element in
subsequent projects by Wright: an apartment house in Chicago (1930),
the Crystal Heights hotel and apartments (1939), and the Price Tower
( ).
The Price Tower, the only built project, is essentially a variation of St. Mark’s.
The Chicago apartment project and the Crystal Heights hotel can be generated by rules that repeat and shift the St. Mark’s plan.
The generic plans of buildings and projects by Frank Lloyd Wright:
a. the St. Mark’s-in-the-Bouwerie apartment building
b. the Chicago apartments
c. Crystal Heights hotel and apartment complex; and
d. the Price Tower

9. For example, below is a schematic version of the St.Mark’s plan, and
one of the rules for generating the Crystal Heights complex. 

10. Wright’s exploration of St.Mark’s as the generator of projects can be
extended readily. Many other interesting and practicable design
possibilities can be generated by modifying the previous rule.
For example, the rule
can be changed by rearranging the shapes to create this new rule  

11. The new rule can be labeled to control how it is applied.
Below are four labeled versions of the rule.
For each rule above, generate a design by applying the rule
recursively to an initial shape which is the shape on the left-side.
(a total of four new designs).  
(a)
(b)  
(c)
(d)

12. 3. Discovering a shape grammar
Below are three designs.
a. For each design, write a shape grammar that generates the design. For design (i), only one unlabeled rule is necessary. For design (ii), only one unlabeled rule is necessary. For design (iii) only two unlabeled rules are necessary.
b. Show a step-by-step derivation of each design using your rule(s).
(i)
(ii)
(iii)