Architectural Doughnuts: Circular-Plan Buildings, with and without Courtyards
2015-09-03 03:00:00 AM
Abstract
An ‘architectural doughnut’ is a building with a plan consisting of two concentric circles. Two types are distinguished: the ‘ring doughnut’ where the central circle is a courtyard, and the ‘jam doughnut’ where some important central space (the ‘jam’) is surrounded by a ring of smaller spaces (the ‘dough’). The main emphasis is on the second type. A series of historical examples is discussed including locomotive roundhouses, Panopticon prisons, hospital wards, parking garages and offices. The ratio of the diameters of the circles is shown to be important for the functioning and even the feasibility of ‘jam doughnut’ plans, depending on the activity housed. In several of the case studies the doughnut shape results in serious inefficiencies in the use of space. Such plan types were soon abandoned. Geometrical data on all the examples are presented in a ‘morphospace’ or world of possible doughnut plans.Mulling Over Shapes, Rules and Numbers
2015-09-01 03:00:00 AM
Abstract
This paper explores the relationships between geometric constructability, numbers, shapes and shape grammars. Shapes are based on compositional constructs in geometry, which rely upon drawing instruments. Implementing shape grammars relies upon numeric encodings, properties of which specify whether shape algorithms are decidable and/or tractable.Shapes and Other Things
2015-08-22 03:00:00 AM
Abstract
Shape grammars have offered a unique computational theory of design over the past forty or so years. Although the focus of shape grammar theory has been on shapes and designs, the material objects or things that might comply with shapes have also been considered. In this paper, I trace the history of approaches for specifying material properties and things through shape grammars. I identify early trends and their limitations, and then propose a new possibility. In early approaches, material things were viewed through the lens of shapes. I argue for a new approach in which shapes are viewed through the lens of material things. Shape grammars are adapted to define making grammars for computing things. Shapes are just one of many things that can be made with these grammars. I conclude with a discussion of the relationship of designing and making, and suggest that designing is a kind of making.Leon Battista Alberti as Author of Hypnerotomachia Poliphili
2015-08-20 03:00:00 AM
Abstract
The enigmatic Hypnerotomachia Poliphili published anonymously in 1499 has long posed puzzles for historians and other scholars. This present text argues that the volume can credibly be attributed, not to Francesca Colonna as is often done, but to the Renaissance humanist and polymath Leon Battista Alberti. Evidence for this is found in the unravelling of arithmogrammatical evidence sprinkled throughout the work, similar to those found in other of Alberti’s works.Pinwheel Patterns: From 2D to 3D Schemas
2015-08-18 03:00:00 AM
Abstract
Pinwheels are generic configurations in architectural layout planning. Planar pinwheels provide familiar schemes for layouts which present design ‘in the round’ with a cyclic symmetry. The paper examines the 3-D versions of 2-D pinwheels where a ‘locked’ joint with three rectangular volume elements aligned along orthogonal axes is a characteristic feature. Pairing handed versions of these locked joints yields a candidate for a 3-D pinwheel schema with six repeated volume elements and threefold cyclic symmetry. Shape rules, based on spatial relations between volumes, generate this and other examples of 3-D pinwheel schemas. These schemas are set in a wider analysis of the numbers and types of joints in 3-rectangulations in terms of maximal bounding planes. The bounding-plane views of the arrangements is set alongside more functional volume descriptions which enables the elements and relations in architectural form to be (re)generated and (re)interpreted both ‘in view’ and ‘in use’.Competition in the Built Environment: Scaling Laws for Cities, Neighbourhoods and Buildings
2015-08-18 03:00:00 AM
Abstract
Built environments at any spatial scale are represented as sets of like objects—cities, neighbourhoods, buildings but also components such as streets, parks, etc.,—which are distributed spatially according to certain rules that we are only just beginning to detect and measure. Unlike normally distributed attributes of the population, these urban elements often scale according to forces that determine large numbers of small elements and a small number of large ones. While many objects evolve from small to large, not all objects can be large as resources as well as physical limits determine the distribution of their sizes. The theory behind such size distributions is referred to as scaling and the shape of such distributions is quite well-defined by various power and exponential laws. As objects grow and evolve, or are even designed, their form changes qualitatively due to the forces of competition and the constraints on space. Here we explore these ideas for cities, neighbourhoods in towns, and buildings, specifically high buildings, revealing that there are both important differences as well as similarities in their form, function, and structure.A Study of the Roughness of Gothic Rose Windows
2015-08-08 03:00:00 AM
Abstract
The rose window is one of the most representative elements of Gothic art and architecture. In this work we analyze fifteen rose windows from fifteen Gothic cathedrals using fractal geometry. Specifically, we examine the texture and roughness of these rose windows focusing on three factors, their designs, glass areas and solid areas. In this investigation we generate parameters which provide a measure of roughness of the rose windows in order to find out if they show a general non-random fractal pattern. The paper concludes that statistically, there is a characteristic fractal pattern in the solid and glass areas of the rose windows of the Gothic style, but not necessarily in their overall design.Typological Descriptions as Generative Guides for Historical Architecture
2015-08-06 03:00:00 AM
Abstract
This paper presents a description grammar approach in the context of the generation of historical architectural typologies. The specific architectural context is classical period Ottoman mosques of the architect Sinan.A Grammar-Based Model for the Mass Customisation of Chairs: Modelling the Optimisation Part
2015-08-04 03:00:00 AM
Abstract
This research presents a methodology to develop and implement a generative design system as the technological model for mass customisation in the furniture industry. The generative design system comprises two subsystems that permit the generation and the evaluation of customised designs within a predefined design language. The shape generation subsystem is defined by shape grammars and parametric design models. The shape evaluation subsystem encompasses simulation and optimisation to guarantee the structural feasibility of the customised designs under operating conditions. This paper focuses on the modelling activities regarding the constitution of the optimisation part of the shape evaluation subsystem. Structural optimisation using simulated annealing is applied to assist the designer in the automatic search for an optimal grammar-based detailed solution. The theoretical model is illustrated by its application to a symbolic mass production problem: Thonet bentwood chairs, which were changed to comply with the mass customisation paradigm.Parametrically Generating New Instances of Traditional Chinese Private Gardens that Replicate Selected Socio-Spatial and Aesthetic Properties
2015-08-01 03:00:00 AM
Abstract
This paper describes the use of a parametric system for generating garden plans that replicate selected socio-spatial characteristics and aesthetic properties of traditional Chinese private gardens (TCPGs). To achieve this, the spatial characteristics of three historic TCPGs are first mathematically derived using connectivity analysis, a variation of a space syntax technique. The data developed through this process is then used to shape the rules of a parametric system to generate new garden plans with similar spatial connectivity values and structures. While these new plans capture some of the socio-spatial features of the TCPG, the other important characteristic of these gardens is a particular level of visual complexity. Using fractal analysis, the characteristic visual complexity of the newly generated garden plans is then compared with the historic cases, to assess the success of the system in aesthetic terms. Through this three-stage process (syntactical derivation, parametric generation and fractal analysis) the paper demonstrates a method for capturing selected spatial and aesthetic properties in a parametric system and also provides new tools for landscape design in the context of specific historical sites and approaches.Schematizing Basic Design in Ilhan Koman’s “Embryonic” Approach
2015-08-01 03:00:00 AM
Abstract
With an outwardly professed interest in mathematics, Ilhan Koman has produced his nonfigurative, abstract sculptures mostly as various series of forms. The difference and similarity between the works in any series is achieved through repetitions and variations of certain relations between parts. This corresponds to creating a relational system and it requires having control over the underlying principles of that system much as basic design students are encouraged to do. In order to substantiate the implications of work such as Koman’s in learning about design thinking, we first delineate the mathematical concepts in Koman’s “embryonic” approach through visual schemas. These visual schemas are then supplied to first-year design students as guides and design constraints as well as tools to formalize their design thinking. We observe that introducing Koman’s schemas to students helps them grasp how they establish relations between parts in their own design processes.Extending the Algebras of Design
2015-07-25 03:00:00 AM
Abstract
Algebras of design have previously been investigated for shapes composed of rectilinear geometric elements, such as lines and planes, and the properties of these algebras have been found to be beneficial for formalising designs, as well as the visual processes used by designers as they manipulate shapes in their design explorations. In this paper, an overview is presented of the application of these algebras in formalising design processes, and this is followed by a discussion concerning issues that arise when the algebras are extended to accommodate non-rectilinear designs, represented by shapes composed of curves, surfaces and solids. Consideration of non-rectilinear shapes introduces new problems not previously identified in the established formalism, resulting from the geometries and topologies of the shapes. These give rise to significant questions about the relationships between shapes and the property of embedding, which is fundamental to the construction of algebras of design.Is the List of Incomplete Open Cubes Complete?
2015-07-16 03:00:00 AM
Abstract
Variations of Incomplete Open Cubes is the major project by the twentieth-century conceptual artist Sol LeWitt. In this paper we interpret the enumerative component of the project as embeddings of graphs. This formulation permits use of an algorithm to check the completeness of the list of the structures produced by the artist. Our conclusion is that the artist found the correct number of structures (that is, 122), but that his list contains a mistake in the presentation of a pair of incomplete cubes, a discovery that appears not to have been noted before.A Vitruvius Inspired Criterion for the Construction of Polygons
2015-07-15 03:00:00 AM
Abstract
A geometric analysis carried out on three homonymous works, known as the Vitruvian man, by Leonardo da Vinci, Giacomo Andrea da Ferrara and Gulielmo Philandro has identified the equilateral triangle as a common feature, differing only with respect to the central position of the apex. Considerations regarding the intended purpose of the tangential outer arc in the Ferrara’s sketch and the possible implications of the two secants, drawn from the mid-point at the base to its intersections with the sides of the square, have provided the basis for a general construction of polygons. The underlying criterion relies on the parameters that define the geometric components of the arc to establish the position of the vertices of the polygon. The fundamental nature of the construction was confirmed through a comparison with an existing procedure by Fletcher, named “squaring the circle”.Cylindrical Mirror Anamorphosis and Urban-Architectural Ambience
2015-07-01 03:00:00 AM
Abstract
Cylindrical mirror surfaces fall into the group of reflecting surfaces that give a distorted image of an object. However, if the object is designed according to the laws of optical geometry, in a way that its mirror image is conceived in advance, then this is anamorphosis. The objective of the present study is to emphasise the potential of cylindrical mirror anamorphosis, in the context of change in the urban-architectural ambience. In this respect it is necessary to obtain a constructive, geometrically correct solution of the 3D model of cylindrical-mirror anamorphosis, whereby the mirror surface is a vertical rotating cylinder. This topic is the primary focus of the present research. In addition, the conditions for change in the anamorphic form were analysed, and its possible functions in architecture were identified. Various examples of existing buildings with cylindrical mirror elements, in respect of which it was possible to construct and apply these types of anamorphoses, were used. The method of constructive perspective and the laws of optical geometry were applied. Analyses were made on the basis of experiments and using AutoCAD 3D methods to analyse the mirror anamorphosis of a cube and octahedron.An Introduction to the Vesica Piscis, the Reuleaux Triangle and Related Geometric Constructions in Modern Architecture
2015-07-01 03:00:00 AM
Abstract
The focus of this paper is the Vesica Piscis, a symbol made from the intersection of two circles of the same radius and where the centre of each circle lies on the circumference of the other. The origin of the Vesica Piscis is uncertain, but it can be found in different cultures throughout many historical periods. The Christian religion was most likely responsible for its spread, first as a fish symbol, then as an architectural niche surrounding sculptures and drawings of Christ, and finally as the Gothic pointed arch. A related geometric construction is the Reuleaux Triangle, which uses three intersected circumferences. In the second half of the twentieth century several architects rediscovered both types of geometrical constructions, producing variations of each. This paper commences with an overview of the history and construction of these geometric forms, and then analyses existing buildings which use them, before discussing different design strategies to develop new mathematical models based on ancient designs.Viewpoints: Mathematical Perspective and Fractal Geometry in Art by Marc Frantz and Annalisa Crannel
2015-07-01 03:00:00 AM
Abstract
Elena Marchetti reviews book Viewpoints—Mathematical Perspective and Fractal Geometry in Art by Marc Frantz and Annalisa CrannelDancing with Isometries in Architecture
2015-07-01 03:00:00 AM
Abstract
This paper aims to emphasize the role of mathematics in computational design education. A computational design process that forces designers to design not only the end product but also the design process itself requires a mind shift to enable the designer to develop algorithms and skills to deal with complex relations. In this context, understanding rule-based systems, generative systems, parametric models and corresponding dimensionalities responding to the forces, variables, patterns, and the mathematics behind them, becomes crucial. Illustrating the reciprocal relationship between mathematics and architecture pattern studies offers great potentials. In this paper, a series of explorations have been presented. In this exploration dance acts as a medium of inquiry into how different complexities can be mapped, how rules can be generative (as first introduced in patterns) and how a set of rules can be transcoded into a complex domain.Leonardo’s Vitruvian Man Drawing: A New Interpretation Looking at Leonardo’s Geometric Constructions
2015-07-01 03:00:00 AM
Abstract
Generally speaking, today’s scientific community considers that the famous figure drawn by Leonardo da Vinci at the end of the fifteenth century was made using the Golden ratio. More specifically, the relationship established between the circle’s diameter and the side of the square is a consequence of the geometric relationship probably discovered by Euclid, but made famous by Luca Pacioli in his De Divina proportione. Aware of the close working relationship between Leonardo and Pacioli, namely in the writing of this last book, the theory that establishes a close relationship between these two figures, making use of this remarkable mathematical relationship, has gained credibility. In fact, the use of the Divina proporzione, despite being a very stimulating construction on an intellectual level, presents too great a margin of error, especially for such a competent geometrician as Leonardo da Vinci was. For that reason, the relationship between these two figures (square and circle) is grounded on a much simpler geometric relationship than the one found at the base of the definition, for instance, of Le Corbusier’s Modulor.Symbolic, Aesthetic and Generative Applications
2015-07-01 03:00:00 AM
Abstract
Co-Editor-in-Chief of the Nexus Network Journal, Michael J. Ostwald, introduces 16 papers in vol. 17, no 2 (2015).
Showing posts with label Nexus Network Journal Architecture and Mathematics. Show all posts
Showing posts with label Nexus Network Journal Architecture and Mathematics. Show all posts
Tuesday, September 22, 2015
Nexus Network Journal Architecture and Mathematics
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