object-e architecture/research

2007-10-17T13:52:00.000-07:00

05. Spiral Study/Helix City
04. Algorithmic Body
-----Voronoi diagrams
-----Example 01
-----Growth (CA + voronoi)
-----Example 02
03. Space_Sound
-----Brownian motion
-----Aleatory distribution of points
-----Cellular automaton
-----Boolean Algebra
02. Lattice Structures with Rigid Joints
01. Cellular Structures

05. Spiral Study/Helix City

2007-10-14T16:56:00.000-07:00

04. Algorithmic Body (voronoi/CA)

2007-10-14T16:55:00.000-07:00

Algorithmic body is an experimentation on growing processes in an architectural context. It aims on one hand to develop an abstract architectural algorithmic process where the initial generative principle is internal to the process itself, without having to rely on aspects of the program or the site. On the other hand tries to test that process with specific examples.

voronoi diagrams

2007-10-14T16:52:00.000-07:00

A voronoi diagram is a way of decomposition or subdivision of space based on an initial set of objects or points (for more information http://en.wikipedia.org/wiki/Voronoi). Voronoi diagrams have countless applications from statistics to biology and urban planning.

[construction method of a 2d voronoi cell]

[several examples of 2d voronoi]

Voronoi diagrams can also be useful in an architectural context, for several reasons:
a. Their structural properties, both in 2d and 3d.
b. As a way to subdivide/organize space, based on proximity/closest neighbor.
c. The fact that they can describe many natural formations, like soap bubbles, sponges or bone cells, which can inform architecture with new ways to organize and structure space.

This project is an attempt to explore the possibilities that voronoi diagrams can provide to architectural design, and to find ways in which they can be used in order to create an architectural process.

In that context, the two main problems that this project tries to study are:
a. a method to construct the voronoi diagrams in such a way that they can be incorporated inside standard 3d packages like rhino or 3dstudio max.
b. a way to define the initial set of points (that are necessary in order for a voronoi diagram to be created).

Concerning the first question, there are already several applications that can be found online. For example a plug in the constructs voronoi diagrams in rhino is already developed and can be found here. (however at the time that this project was developed the plugin was failing to calculate correctly complex 3d voronoi diagrams. A more reliable application is qhull. However custom scripts have to be created in order for the results of qhull to be imported into a 3d software.

[applying different smoothing algorithms to the edges of the voronoi cells]

[using lines as the generators of the diagrams]

References:
-Aranda, B., Lasch, C. Tooling New York: Princeton Architectural Press, 2006.
-Bollobas, B., Riordan, O. Percolation Cambridge: Cambridge University Press, 2006.
-Kim, M.S., Shimada, K., (eds.) Geometric Modeling and Processing – GMP 2006 Berlin: Springer, 2006.
-Klein, R. Concrete and Abstract Voronoi Diagrams Berlin: Springer-Verlag, 1987.
-Okabe, A., Boots, B., Sugihara, K., Chiu, S.N. Spatial Tessellations, Concepts and Applications of Voronoi Diagrams West Sussex: John Wiley & Sons Ltd, 2000 (f.e. 1992).

-----------------------------------------------------------------------------------(next)Example 01

example 01

2007-10-14T16:50:00.000-07:00

Here voronoi diagrams are used initially in order to analyze the existing urban condition of a specific site and to specify the place that the intervention is going to be placed. An urban analysis based on simple voronoi diagrams is one that is based solely on proximity. In other words each point on the map has the same value.

The following animations display the way that the desired movement on the site is manipulated in order to define the shape of a high rise building.

The output of the previous animation is used in order to define the limits within which a new 3d voronoi diagram is generated. The initial set of points that is used is based on program requirements. The use of program elements in order to define the voronoi diagram may be a convenient option, however it is also a too obvious one. In a way it resists the algorithmic nature of the voronoi and tries to rationalize a process that if is left "free" can generate highly unpredictable results. (See sections 03 and 04 for an alternative)

The edges of the voronoi cells become the structure, while a first idea for enclosed space was to use again the voronoi cells (in a 'smoothed' version) as clusters of space in a configuration that resembles the relation of bones to organs.

Voronoi diagrams (previous)----------------------------------------------(next)Growth (CA + voronoi)

growth (CA + voronoi)

2007-10-14T16:48:00.000-07:00

One of the most interesting characteristics of algorithms is that they can be totally self-referential. An internal quality that can produce a process independent and autonomous,that relies only on its own rules. Using program requirements or site elements in order to generate the voronoi diagrams obviously still relies on external factors. Therefore here another algorithm (a cellular automaton script) is used in relation to the voronoi in an attempt to render a process that doesn't have to refer to anything outside itself. A 'growing' process, with its own rules that doesn't have to rely on any external factors (apart from the initial state) in order to be generated.

[growing examples: a cellular automaton used to generate surfaces]

The process that is developed can be described by the following steps:
a. a 2d cellular automaton script is executed, with a random or pre-defined initial configuration of cells.
b. every generation of the ca is stacked on top of the previous ones creating this way a 'progression' of active cells.
c. the centers of the active ca cells are used in order to generate the voronoi diagram. The limit of that diagram is defined by the limits of the outer active cells of each generation of the ca.
d. the edges of the voronoi cells are used as the structural system.
e. a smoothed version of the voronoi cells is used in order to define enclosed space.

[the cellular automaton]

[the active cells of the automaton used as points for the generation of the voronoi diagram]

[the different steps of the process described above]

[photographs of a 3dprinted model of the output.]

Example 01(previous)------------------------------------------------------------------(next)Example 02

example 02

2007-10-14T16:38:00.000-07:00

The process already described is employed in the design of a specific project: a transportation node + shopping mall downtown St. Louis. The ‘node’ connects two metro stations and the train station and at the same time hosts a shopping mall. The building is developed in analogy to the human body: organs/bones/skin. The organs become the enclosed spaces, the bones the structural system and the skin an outer membrane that wraps the other two. The project is employing the latest building technology with a fiber-carbon structure and ETFE pillows for the outer skin.

[exterior perspective]

[interior perspective; the stairs from the train station to the shopping mall]

[view of the train station]

[interior perspective; the shopping mall]

[view of the trai station]

[plan; first level]

[plan; second level]

[longitudinal section]

[3d detail of the structure]

[3d printed model of a part of the building]

[construction detail]

Growth (CA + voronoi)(previous)----------------------------------------------------------

03. Space_Sound

2007-10-14T16:30:00.000-07:00

Space_Sound is a study on the work of composer and architect Iannis Xenakis.
Iannis Xenakis used extensively computation and mathematics in order to create music. The initiative for this project was that while Iannis Xenakis is widely acclaimed and studied as an innovator in avant guard music, his work is not extensively examined in relation to architecture, and when that is done the focus is always on his architectural designs and mostly on the Philips Pavilion. However, Xenakis in his writings was always underlining that his methods in composition are not only applicable to music, but also to the visual arts and most notably to architecture.

Xenakis’ musical scores are composed in such a way that they have an underlying spatial dimension. His scores and diagrams for his compositions share very little resemblance to conventional musical sheets, while they could be undoubtedly “read” as spatial diagrams and architectural blueprints.

Xenakis was one of the first researchers to use computers in his musical/mathematical explorations. With a delay of some decades, the use of the computer in composition reached also the field of architecture and eventually led to a more constant, or more obvious, impact of mathematics to architecture. The architectural avant guard today has to deal with, up to a certain extent, with mathematical or computational processes like cellular automata, L-systems, stochastic process and boolean algebra, all methods employed earlier by Xenakis in his work.

Having the above in mind, Xenakis’ work could prove itself extremely helpful in relation to the questions that computation is posing to architecture today. More specifically, Xenakis’ work could provide insights for architectural practice in relation to the computers in two ways:

a. First in a theoretical level. Xenakis provides a very extensive philosophical and theoretical background for his work through his writings, which seems possible to be used also in relation to architecture today.

b. Secondly in a design oriented level. Iannis Xenakis started to use mathematics and computers as his tools for composition in the beginning of the 1960’s and continued this research until the end of his life. Therefore his work has to offer a great variety of methods, techniques and processes for the musical composition. Given the fact that Iannis Xenakis’ way of working with music was based on ‘spatial’ techniques and visualization of his ideas through drawing, a study of his projects could offer precious insight for architectural design. In addition to that, the introduction of those spatial qualities in Xenakis’ research that focuses on sound, arises questions on the relation between space and sound and how the one discipline can offer resources to the other.

So, space_sound consists mainly of visual representations of several methods that Xenakis employed in his work. Through scripting concepts and mathematical ideas like boolean algebra, alleatory distribution of points on a plane, brownian motion, cellular automata etc. are used in order to create small animations that are trying to explore the spatial or architectural qualities that those concepts can activate.

brownian motion

2007-10-14T16:27:00.000-07:00

( >> N’Shima)

Brownian motion is a mathematical model used in order to describe the movement of particles inside fluids. Although the motion of the particles is described from various ‘brownian equations’ it can not be predicted. Therefore Brownian motion can be used in order to produce randomness.
Xenakis is employing Brownian motion in N’Schima in the context of stochastic process that he constantly applies in his compositions as the means to create randomness. In N’Schima Brownian motion is defining the glissandi that the various instruments are following.

aleatory distribution of points on a plane

2007-10-14T16:25:00.001-07:00

( >> diamorphoses)

Aleatory distribution of points on a plane is a stochastic process, that is a process that is characterized by randomness, where a specific number of points are distributed on a plane in a way that satisfies specific rules.

cellular automaton

2007-10-14T16:20:00.000-07:00

( >> Ata, Horos)

A cellular automaton is a discrete model, which means that they don’t require the notion of continuity. Cellular automata have many applications in mathematics, computation and biology. A cellular automaton consists of a grid where each cell may have two states, empty of full (0 or 1) and a specific set of rules that defines the way that the state of the cells is changing over time. After the rules are applied to all the cell of the grid a new generation is created. Those rules are always in relation to the neighbor cells of each cell. That is the state of each cell in generation n is defined by the state of its neighbor cells in generation n-1. One of the most famous set of rules is Conway's Game of Life:
1. Any live cell with fewer than two live neighbors dies, as if by loneliness.
2. Any live cell with more than three live neighbors dies, as if by overcrowding.
3. Any live cell with two or three live neighbors lives, unchanged, to the next generation.
4. Any dead cell with exactly three live neighbors comes to life.

One of the most interesting properties of the cellular automaton is that it requires no input from the user (therefore an automaton). It is a self referential process where the output of each generation is becoming the input for the next one. What is also interesting is that from a very specific and simple set of rules, when we let the automaton to evolve, we can produce very complex formations.

Xenakis used cellular automata in many of his later works, for example Ata and Horos, in order to create new harmonic progressions.

(the following animation uses the life.mel script from nthd.org)

boolean algebra

2007-10-14T16:00:00.000-07:00

( >> Herma, Eonta)

Boolean logic is a system of logical operations. Those operations are union, subtraction and intersection.

02. Lattice Structures with Rigid Joints

2007-10-14T15:53:00.002-07:00

01. Cellular Structures

2007-10-14T15:53:00.001-07:00

Technological developments have multiple results in relation to architecture. The ability to observe at the micro level surely falls into this category: Cells and microbiological structures are offering a whole new world that can help as develop new spatial relationships and understand space in a different way. And that goes well beyond mere formal explorations. Cells of course are displaying unique forms that could be transferred to architecture, but are also displaying ways of organization, ecological strategies and extremely efficient structural systems, all of which can inform architecture in different levels.

This project explores the way that a specific cell functions: Xylem vessels are cells that are present in most plants. Their function is to transfer water from the ground to the upper part of the plant. The images above show several digital models of the cells that explore the way they are formed and structured. The following animation displays the way that the cell function.

One single unit of the cell is isolated and manipulated in order to be transformed into something new, that on one hand will share the formal language and some properties of the cell, on the other hand it will have a new function in an architectural context. The cell is transformed into a rain collector:

The unit (the rain collector) is multiplied again and a system of rain collectors is formed. A structural system that would support the collectors is also generated. The follow animation explain the way that the structure was generated.

The collectors were generated thought a dynamic "animated" process. The result is also dynamic: The collectors are opening or closing giving this way the possibility to the user to control the collection of the water.

test

2007-10-12T08:12:00.001-07:00