The paper is divided into four parts. Part I identifies fundamental theoretical problems, contrasts the application of computation to architecture and to music, and draws upon several different areas for insight into the nature of making; Part II reviews particular architectural implications of these considerations, introduces the concept of computational composition in architecture, and presents a brief overview of important precedents; Part III proposes new goals for computer-aided architectural design and presents a framework for computational composition; finally, Part IV presents recent work directly related to the ideas presented in the previous parts and leads to the Conclusion. The appendices contain a pseudo-Prolog expression of Alvar Aalto's architectural language and notes on features of the PADL-2 solid modeler that are architecturally interesting.

Mathematics and especially geometry have found increasing application in the computer-based design environment of our day. The computer has become the central tool in the modern design environment, replacing the brush, the paints, the pens and pencils of the artist. However, if the artist does not master the internal working of this new tool thoroughly, he can neither develop nor express his creativity. If the designer merely learns how to use a computer-based tool, he risks producing designs that appear to be created by a computer. From this perspective, many design schools have included computer courses, which teach not only the use of application programs but also programming to modify and create computer-based tools.

In the current academic educational structure, different techniques are used to show the interrelationship of design and programming to students. One of the best examples in this area is an application program that attempts to teach the programming logic to design students in a simple way. One of the earliest examples of such programs is the Topdown Programming Shell developed by Mitchell, Liggett and Tan in 1988 . The Topdown system is an educational CAD tool for architectural applications, where students program in Pascal to create architectural objects. Different examples of such educational programs have appeared since then. A recent fine example of these is the book and program called “Design by Number” by John Maeda . In that book, students are led to learn programming by coding in a simple programming language to create various graphical primitives.

However, visual programming is based largely on geometry and one cannot master the use of computer-based tools without a through understanding of the mathematical principles involved. Therefore, in a model for design education, computer-based application and creativity classes should be supported by "mathematics for design" courses. The definition of such a course and its application in the multimedia design program is the subject of this article.

Our results fall in three major categories: 1) pedagogical discoveries about learning to design with a computer, which is greater than the sum of learning to design and learning about computers; 2) design exercises based on the Macintosh environment, exploiting the unique graphic qualities of the machine while simultaneously developing the ideas and drawing skills needed in the preliminary stages of design; 3) descriptions of the studio environment, including hardware, software, workstation layouts, security solutions, and other practical information that might be useful to others who are contemplating a similar project.

The "Calor" problem requires the move of a famous residence to a hot arid climate. The residence must then be redesigned in the original architect's style so the building becomes as energy efficient as possible in its new arid environment. The students are required to use as design criteria a new building program, the design philosophy of the original architect, and appropriate passive energy techniques that will reduce the thermal stress on the building. The building's energy response is measured by using an envelope energy analysis program called "Calor".

Much of the learning comes from imposing a new set of restraints on a famous piece of architecture and asking the student to redesign it. The students not only need to learn and use a different design philosophy, but also develop new skills to communicate their ideas on the computer. Both Macintosh and IBM computers are used with software ranging from Microsoft Works, Superpaint, AutoCAD, MegaCAD, Dr Halo, to Calor.

We are left on the horns of a dilemma. The rapid response and exciting images of the computergenerated video environment suggest we are entering an era when architecture itself becomes electronic. The physical built-form recedes in importance, and may even become redundant. But we must also ask: Are we entering a post-computer age? Will we realize the potential profundity of our innate human biocomputers - to the point where we renounce the hard technology of the material for the soft technology of consciousness?

Using color is among the more difficult of traditional studio chores -- it is not difficult on a computer. The manipulation of color can be a simple task if one is given reasonable software and a good graphic computer. Once introduced to students, the techniques for coloring elements on a computer find acceptance as a design tool. Methods can be quickly found for modifying the perception of space and form through the use of colon

Modern architecture is rooted in the study of color as a generator of form. This idea permeated the teachings of its founders. Yet modernist concern for color has over time evolved into a pedagogy of space and form at the exclusion of color, so much so that the modern movement today stands accused by its detractors as being formed in many shades of grey.

Modern architecture is not grey! This paper will illustrate how, using the modern graphic computer, color may be introduced to the studio and discovered as an element of design and as the substance of architectural form giving.

The energy performance of a base case building in each of four climates and cultures is presented. The climates are: Phoenix (hotdry), Minneapolis (cold-dry), Boston (cold-humid), and New Orleans ( hot- humid). Keeping the host climate, site, building size and function constant: but varying materials, shape and design concepts, each base case is iterated through a series of computer assisted re-designs to transform each base case building into an architecture representative of its regional climate and culture.

Traditional technologies and concepts produce traditional regional architecture. New technologies and concepts produce forms expressive of an emerging high-tech, high-touch, low energy society.

The paper presents computer generated work by the author and his students. It also presents an interim evaluation of the successes and difficulties of conducting a 'paper free' design studio.

Architects are creative problem solvers, primarily driven by intuition, while coming from a sense of the past and the logic of the present. Our initial attempts at integrating computing into the studio, as evidenced by this collection of papers, is very diverse, based on differing pedagogical assumptions, and the achieving of significantly different results. This would appear to be evidence of a revolutionary approach to the problem rather than a scientific evolutionary approach. Terrific! This is when we as architects are at our best. Although we reach a great number of emphatically dead ends, the successes and discoveries achieved along the way are significant.

The diversity and quality of papers submitted suggest that we are indeed pursuing the task of integration in our typical, individual, intuitive, logical manner. I commend all of the authors who submitted proposals and thank them for expanding the envelope of integration into their personal exploration.

Computer programs exist that are well suited for this purpose, two of which are described. They offer a broad range of design capabilities, and are easy to master because of their intuitive and graphically oriented approach.

A number of examples are given to illustrate the potential of computer-aided learning as a complement to traditional methods either in the classroom or in coursework.

The presentation will present our experience to-date in using conventional computer graphic tools to represent design ideas and contrast it with a video demonstration of our prototypical dynamic urban design modelling software for the Silicon Graphics IRIS computers.