L March

Urban space and structures

Part I. Explorations: Introduction 1. The grid as generator Leslie Martin 2. Speculations Leslie Martin, Lionel March and others 3. Elementary models of built forms Lionel March 4. The use of models in planning and the architectural design process Nicholas Bullock, Peter Dickens and Philip Steadman Part II. Activities, Space and Location: Introduction 5. A theoretical model for university planning Nicholas Bullock, Peter Dickens and Philip Steadman 6. The modelling of day to day activities Nicholas Bullock, Peter Dickens and Philip Steadman Part III. Urban Systems Introduction 7. Models: a discussion Marcial Echenique 8. Development of a model or urban spatial structure David Crowther and Marcial Echenique 9. A structural comparison of three generations of New Towns Marcial Echenique, David Crowther and Walton Lindsay Afterword Bibliography.

The Method of Residues in Urban Modelling

This paper seeks to extend the macrostatic approach to urban modelling by treating modelling problems as many-stage processes. Within such a process the early stages are concerned with explaining the relatively trivial characteristics of the phenomena of interest, and the later stages are devoted to explaining more important behavioural issues. Coleman (1964) calls this approach the ‘method of residues’, and its power is first demonstrated here by a reinterpretation of the well-known gravity model. An ad hoc test of the method on the Toronto-centred region serves to emphasise the need for a more formal approach, and thus an analogy between the method and the Bayesian viewpoint is introduced. A method of information minimising, more general but consistently and unambiguously related to the method of entropy maximising, is used to make the formal approach operational, and the method is used to generate an ‘extended’ family of spatial-interaction models. A number of spatial-interaction models are derived, and the paper is concluded by a test of two of these models on the Toronto-centred region.

Spatial Systems in Architecture and Design: Some History and Logic

In the past decade, a powerful generative approach to shape and spatial systems has been developed in parallel with the introduction of computer aids in the design process. This new approach allows for designs and their meanings to be viewed as the results of computations carried out according to rules of composition and correlative rules of description. Some of the history and logic of these developments is surveyed in this paper.

On Counting Architectural Plans

This paper demonstrates the one-to-one correspondence between trivalent 3-polytopcs and fundamental architectural schemes. Enumeration results from the literature of combinatorics are given and are related to the problem of counting various classes of architectural plans and their adjacency structures. This work is related to recent architectural research by other authors: Mitchell et al (1976), Korf (1977), and Lynes (1977), The foundations are laid for a mathematical theory of architectural planning.

Architectonics of proportion: a shape grammatical depiction of classical theory

A shape-grammatical interpretation is given for the anthyphairetic procedures of Platonic mathematics.

Babbage's Miraculous Computation Revisited

Charles Babbage used an example suggested by the computational power of his calculating engine to suggest that ‘miraculous events’ might be as lawful as the regularities presumed by ‘vast inductions’. In this paper I revisit the issue by employing a simple shape grammatical example. Induction and emergence are contrasted.

Architectonics of Proportion: Historical and Mathematical Grounds

With the intention of reevaluating proportion theory in design, I provide here a grounding for a pictorial approach to the anthyphairetic procedures of Platonic mathematics.

On Ho's methodological approach to design and planning

The work of Y-S Ho is placed in the context of design and planning theory. The significance of the Galois lattice methodology is stressed.

The Smallest Interesting World

Within a set-grammatical frame, multiple structures are determined for a line by using an object–feature approach. The Galois connection and its related lattice is employed. Most ‘world-pictures’ of the line are not Boolean.

Renaissance mathematics and architectural proportion in Alberti's De re aedificatoria

This paper sets Albertis rules of architectural proportioning in the context of Renaissance mathematical practice. While Alberti makes didactic use of the well developed theories of harmony from music, it is shown that his architectural usage is not analogous to musical systema, even though the arithmetical foundations are shared. The common base for fifteenth-century musical theory and Albertis architectural recommendations is Pythagorean arithmetic, derived largely from Nicomachus. Alberti also develops a geometrical approach involving magnitudes derived from the cube. Neither the diagonal of a face, nor the diameter of the sphere which circumscribes the cube are commensurable with its side. Alberti makes use of rational estimates for the square roots of two and three, and these ratios are evident in his work. Some examples are indicated for the purpose of linking theory to practice, but it is not the intention of this paper to analyse specific buildings in depth. The purpose of the paper is to suggest a potent theoretical frame within which future empirical investigations might flourish.