What shape is this grammar?

The exploration into means for designing images for the recombinable vector graphics library led me to a foray into the field of shape grammars. This text is of an exploratory nature, and by no means a finished work. This means that some topics are thinly explored, and others may not be thoroughly thought out. Any comments, corrections or suggestions are more than appreciated!

Shape grammars form algorithmic systems for design through computations with shapes. Essentially, shape grammars form a set of rules for operations on shapes, that can be used to create compositions by addition, subtraction, rotation etc. They were invented in the 70’s by George Stiny and James Gips, originally in the context of specifying formulas for abstract paintings. Gips states in the paper in question that their goal was to devise a formal method for creating “good art”.

Shape grammars are useful for generatively constructing complex compositions based on simple rules. This applies especially to architecture, which explicitly deals with a domain of shapes, spaces and volumes. For this purpose of creating rule-based variations of architectural compositions, several computer programs have also been made.
Shape grammars have indeed seen most applications in the field of exploratory architecture, for instance used by architects like Rem Kolhaas and Steven Holl.

Simmons Hall dormitory, Massachusetts Institute of technology, by Steve Holl, was designed by utilizing shape grammars.

Graphic design resembles architecture as it on an abstract level is the ordering of forms in space and time, according to certain rules. This is obviously no original observation, but as far as I am aware there has been very little research in systematic formal approaches in the field of graphic design. I have so far been unable to find if shape grammars ever have been used for analyzing or quantifying graphic design.


A cover design by Richard Paul Lohse in the style of Neue Typografie.

Strict systematic approaches are legio in graphic design though, like the Neue Typografie, but they have not been formalized and used as a base for further research and experimentation. Instead, it seems that the field of graphic design is mostly accumulating complexity by rejecting some methodologies in favor of new ones, only to later on eventually allow for coexistence and happy bastardisations of these different methodologies.

The practice of graphic design often owes much to free artistic approaches, and overly systematic methods are frequently frowned upon as modernist rigidity. However, most graphic designers, modernist or not, work with a certain set of methods for each project – even though they often are not explicitly defined, but rather hidden away in the designer’s implicit understanding of her work. These methods could well be called design algorithms.

Even whimsical digressions from the design rules in a particular project can be thought of as algorithms. These intimately relate to the decisions governing the entirety of the project, as every page in a book or a magazine mostly isn’t it’s own, isolated rule. A designer thus tends to think of how these sidesteps happen, when they happen, and how they relate to the normal pattern of the design project.

One can make a rough idea on the set of algorithms used in book design, for instance. Firstly, we conceive of a book as a physical object. It has dimensions that form the spatial constraints for the design. Each part of the book will have its own character, that can be defined as a certain algorithm tree. These will in some way be interrelated as components of the structure of the book in its entirety.

The most basic form of an ordinary book is probably that of a novel without illustrations. It basically has the following set of parts, in the progression that can be seen as a linear walkthrough in order of reading:

•The definitions of size, binding and physical properties like paper etc.
•Cover design and layout and how these spaces are treated.
•The main text block:
–Front matter like copyright pages and tables of content.
–Chapter openings
–Chapter text flow – the progression of the design in time
–Chapter endings
–Eventual end matter, ending of book.

All these parts interrelate, and they all usually need to have their own systems of design that defines how every element on the page is treated. If there happens to be pictures in the book, or maybe different types of text (like poetry or tables) the complexity of the tree increases, and one needs to consider for instance things like a picture on a  chapter opening page. Luckily, a reasonably experienced designer can derive these instances from the base one of the text flow, and doesn’t have to come up with every single one from scratch.


In classical book design, like the approach advocated by the eminent Robert Bringhurst, the set of algorithms is tightly bound and all books form close variations on a theme. The hierarchy of letter style above, from The elements of typographic style, illustrates this. Additionally, the systems for creating different parts of the book are essentially rather minor variations on the same algorithm. These are the fugues of book design, admittedly a very conservative art.


An even better example of what is essentially a collection of book design algorithms is the pinnacle of teutonic orderliness called Lesetypografie, a page pictured above, by Friedrich Forssman and Hans Peter Willberg. This book contains a large, thematic collection of examples and methods on how to approach different parts of several subtasks in book design. The authors state explicitly that the book is not to be used as an how-to-design or a bible of absolute rules, but as a repository of recipes for variation.

Essentially – the authors supply algorithms, but not the exact parameters, and the reader or user is encouraged to sample, play with and cross-breed them. However, it can be noted that the extent of Forssman’s and Willberg’s achievement is such, that the book still has garnered something of a bible-like status in the german-speaking world: If it is not in Lesetypo, you can’t do it.

What Bringhurst teaches is suggestions on how to use design algorithms, even though he doesn’t use that term.  The central aspect of generative or algorithmic design is that creativity primarily goes into devising or modifying a method, which is then executed. Even though a generative or algorithmic approach hasn’t explicitly applied, it can be a very useful way of creating post-hoc descriptions.

Shape grammars have for instance been successfully used to describe the plans of Palladian villas, Frank Lloyd Wright’s prarie houses, and islamic tiling patterns. Whether this accurately describes the methods originally used in design is not necessarily relevant, if the description manages to accurately explain the variations in patterns.



The formulas for the Palladian villas can subsequently be used to create an endless variety of different plausible housings for more or less well-to-do romans – some of the plans in the above picture are such speculative villas. Similarly, one could devise more prarie houses belonging to the same domain. It isn’t too far-fetched to imagine that a similar approach using shape grammars could work in the field of layout and typography.

A problem in current graphic design is in my opinion the difficulty of defining and trying different algorithms. Desktop publishing has considerably simplified the craft of layout, and created boundless possibilities for compositions. On the level of devising algorithms, however, the techniques haven’t advanced much from the times when paste-up layouts were still the norm. Desktop publishing programs have reorganized the tasks of graphic design, but for the most part not essentially transformed them.

It is of course easier to try out ideas in test settings that look like finalized results, but current layout programs don’t give a hand in coming up with variations on layout systems. Therefore many still find it easier to sketch ideas of grids and text settings on paper, as this can be the fastest method for rough prototyping.

* * *

The recombinable vector library is more about shapes and their meanings, than abstract compositions. Even though shape grammar can be used to describe pictures, it does not appear as an immediately promising method for creating them. The main reason is that a representational scene is a top-down structure, whereas shape grammars are more suited for generative bottom-up approaches that create emergent compositions from simple algorithms. In other words, the shape grammars are ideal when you don’t care about the end composition as such, but rather about the relations between the parts that form it; whereas in a representative image, the end result is exactly what you care about.

It can be argued that an illustrator also uses algorithms, after a fashion, when creating an image. However, the domain of illustrating (here used specifically referring to image creation by hand) is much more fluid than the ones of layout or architecture. A post-hoc systematic specification of even a simple line drawing is easily very complicated in comparison to the ease with which the work was created. The prospect of using parametric methods to create illustrations that emulate hand-made work seems indeed quite distant.

The fluidity of the domain of illustration can also be seen in that there are few successful attempts at defining methods for illustration, compared to graphic design or architecture. If you read Bringhurst and apply a selection of his methods rigorously to a project, you should end up with a well-designed book in the classical vein. It is hard to imagine how something similar could be achieved with a book on how to illustrate.

Knight, T. 2000. Shape grammars in education and practice. Department of Architecture, MIT,Cambridge, MA,
Stiny G, Gips J, 1972, “Shape Grammars and the Generative Specification of Painting and Sculpture”, in C V Freiman (ed), 1972,Proceedings of IFIP Congress71, Amsterdam: North-Holland 1460-1465. http://www.shapegrammar.org/ifip/ Retrieved 4.9.2009.
Özkar, M. and Kotsopoulos, S. 2008. Introduction to shape grammars. In ACM SIGGRAPH 2008 Classes (Los Angeles, California, August 11 – 15, 2008). SIGGRAPH ’08. ACM, New York, NY, 1-175.  http://doi.acm.org/10.1145/1401132.1401182


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