Section 3 Shape Grammars The Design Space of Schematic Palladian Plans for Two Villa Topologies Thomas Seebohm University of Waterloo, Canada Dean Chan University of Waterloo, Canada Abstract Given the plan topology for the layout of the rooms of a Palladian villa, we ask what is the design space of possible Palladian plans. What does this space look like in terms of dimensions and proportions? Two plan topologies are exam- ined to throw some light on this question. One is that of the Villa Angarano while the other is that of the Villa Badoer. A Maple program was written for each topology to solve the equations for room proportions, to cycle through the possible proportional spacing of the underlying Tartan grid, and to plot out the possible plans in the design space. The programs eliminate from the design space those alternatives that violate basic Palladian constraints, such as no room having an aspect ration greater than 2:1, and such additional con- straints that we and other authors have found. A selection of the plotted output of plans in the design space for each topology is presented as well as three- dimensional plots showing the number of plan alternatives in different regions of the critical parameter space, namely, the length and aspect ratio of the plan. We believe that this is the first instance of enumerated Palladian plans which goes beyond topology to examine issues of dimension and proportion. One conclusion is that one cannot scale a Palladian plan topology to fit any set of overall dimensions. Keywords Palladio, Design Space, Villa, Plans, Rule-Based Generation 156 2001: ACADIA Thomas Seebohm The Design Space of Schematic Palladian Plans for Dean Chan Two Villa Topologies 1 Introduction typologies. Here we are using the term, design In 1978 Stiny and Mitchell developed a shape space, in the sense that it is used in information grammar, a set of graphical rules, to encapsulate science as the collection of design alternatives. the style of Palladian floor plans in designs gen- What we would like to demonstrate in this paper erated by the grammar. This is probably the first is what the design spaces for these two typologies attempt to apply the concept of shape grammars are like: How many designs do they each contain to architectural style. (Stiny and Mitchell, 1978). and what do they look like? Providing a better Stiny and Mitchell proved the viability of shape understanding of design spaces is of great impor- grammars for representing style by demonstrat- tance to future computer based design systems ing that several known Palladian villas can be gen- which might assist a designer with stylistic guid- erated by the grammar and that some possible villa ance in laying out designs and in detailing with- plans generated by the grammar were also con- out the designer having to worry about every de- vincingly Palladian. They did not prove or dem- tail. We do not think that rule-based generative onstrate that every plan generated by the gram- design systems will be able to design without hu- mar was convincingly Palladian. As Hillier has man intervention simply because the design space pointed out is usually very large. Consequently, the job of the “In the last analysis, architectural theory is a matter designer is to select from a vast design space. It is of understanding architecture as a system of possibili- through the provision of constraints over and ties, and how these are restricted by laws which link beyond those that define a particular style that a this system of possibilities to the spatial potentialities of design for a specific site and client comes about human life. At this level, and perhaps only at this level, (one can say that, in effect, what designers nor- architecture is analogous to language. Language is of- mally do is to select from a vast design space my ten naively conceptualized as a set of words and mean- means of trained intuition). ings, set out in a dictionary, and syntactic rules by which Now Stiny and Mitchell’s shape grammar is a set they may be combined into meaningful sentences, set of shapes and rules for the spatial relationships out in the grammars. This is not what language is, between the shapes. To use the language analogy, and the laws that govern language are not of this kind. one can say that the shape grammar contains both This can be seen from the simple fact that if we take the words of a language and the syntax. The gram- the words out of the dictionary and combine them in mar includes some constraints, in the form of la- grammatically correct sentences, virtually all are ut- bels and markers, which restrict when the rules terly meaningless and do not count as legitimate sen- can be applied. One can think of these constraints tences. The structures of language are the laws which as local constraints because they influence the restrict the combinatorial possibilities of words, and emerging design locally where a rule is applied. through these restrictions construct the sayable and the In view of the local nature of the built-in con- meaningful. The laws of language do not therefore straints one cannot expect these constraints to say tell us what to say, but prescribe the structure and lim- anything about the overall design. It may well be its of the sayable. It is within these limits that we use that there should be some constraints operating language as the prime means to our individuality and at the overall level of a design to distinguish Pal- creativity.” (Hillier, 1996) ladian from non- or neo-Palladian designs. It is This quotation from Hillier frames the issues to also at this overall level that a designer would be explored in this paper by means of a detailed choose one design over another in the design study of two particular Palladian plan typologies, space to select a design most suitable for a par- namely the typology of the villa Angarano and ticular client and site. Mitchell has described this that of the villa Badoer. We will be looking at the process as one of applying predicates to determine issue of constraints (“the laws which restrict the if designs are acceptable (Mitchell, 1990). Now combinatorial possibilities”) and how this reduces the question is whether or not the Palladian shape the “system of possibilities”, that is to say, the grammar should include some constraints oper- design space of possible Palladian plans for those ating at an overall level to limit the design space 2001: ACADIA 157 Section 3 Shape Grammars of possible plans to Palladian plans. Does it in- that can generate Palladian (including some non- clude non-Palladian plans? Palladian) plans and corresponding elevations. To answer this question, consider briefly the struc- Unlike the Stiny and Mitchell approach, Hersey ture of Stiny and Mitchell’s Palladian grammar. and Freedman include specific dimensions right The grammar begins by laying out a tartan grid. from the start by a specification of the length and As Wittkower showed in 1949 (Wittkower, 1949), width of the overall plan. A specific layout is then the plans of Palladian villas can be thought of as generated by a series of vertical, horizontal and being underlain by a tartan grid along which the combined vertical/horizontal splits. The propor- walls align. Palladio, in the Four Books of Archi- tions used for the splits are based on the propor- tecture, always laid his plans out with the axis of tions and the probability with which Palladio used symmetry running vertically. Given that all Pal- them. Hersey and Freedman’s software does not ladian plans have a large room, the sala, on the therefore lend itself to systematically enumerat- axis of symmetry, the underlying tartan grid must ing possible plans but it does show, if one gener- have an odd number of cells running horizon- ates enough plans, what Palladio was likely to do. tally. Possible grid dimensions that Palladio has It immediately becomes clear that the Palladian used are 5x3, 5x4, 3x5 and 5x6, where the first shape grammar does not contain sufficient con- number is the horizontal number of cells. Next straints to generate only Palladian plans. Indeed, Stiny and Mitchell concatenate some cells and even at the level of topological possibilities, it is possibly shift some walls off the grid. All the rule clear that some, such as plans with rooms that span applications up to this point define the topology the entire plan are not Palladian. More impor- of the spaces. On this basis Stiny and Mitchell tantly, however, Hersey and Freedman show that have enumerated all the possible Palladian plan inclusion of dimensions brings out the need for topologies for 3 x 3 and 5 x 3 topologies (Stiny these constraints, some of which are local in na- and Mitchell, 1978a). After the basic topology of ture and some of which affect the overall plan: the room layout has been derived, additional rules · No room dimensions is less than seven Vicentine feet are applied for the following (Mitchell, 1990): · The ratio of the smallest to the largest room area is 9 or less. · Exterior wall definition and detailing · No room should have an aspect ratio greater than 2:1 · Principal entrances and wall inflections · Rooms on the axis of symmetry tend to be larger than · Exterior columns adjacent ones · Windows and doors · Other rules that they discovered are: · Terminators (determine when rule application ceases). · The total number of rooms in a plan is equal to or less than 20. A commendable feature of the Stiny and Mitchell · The total number of interior rooms without windows shape grammar is that it is parametric, meaning is equal to or less than 4.