Algorithms in Design of Architecture: Aesthetic or Scientific

What does algorithmic architecture mean?? It might be the ones which are designed with algorithms. Ones with Mel scripts. The others with Rhino scripts. At the circumstances, various architecture generated by manipulating algorithms can be seen in many scenes including competitions, student’s works, etc. However, are such applications to design really enough in terms of potentials of computation? The answer for me is “No”. Although proliferation and differentiation might be successfully completed with algorithms so far, the true benefit derived from uses of computers is not probably acquired.

Just at that moment, the Earth is facing one of the most critical moments in its history, which is an environmental problem. Various elements such as changes of air temperature, sea-surface rising, increases of CO2 emissions, and so on. As far as concerned about such problems, what are social responsibilities in architectural field? In my mind, computation in architecture would be one of the most important factors in future in terms of solutions toward environmental problems. “Not only aesthetic, but also scientific,” this is my concept which is always contemplated at present. In other words, final aim is the fusion between sensation and beauty, and science and rationality.

There are several interesting examples in relation to uses of algorithms in terms of environmental factors. John Frazer is a pioneer in computation and architecture, who started to research at the Architectural Association School of Architecture in 1960’s. His book “An Evolutionary Architecture” is one of his research results, which can be downloaded freely from the aaschool website. In addition to him, Indian architect, Manit Rastogi who is cofounder of Morphogenesis and actually was one of former students of John Frazer at aaschool, completed environmental algorithmic architecture recently. The building is formed in relation to sunpath and glare.

Voronoi Diagram

Voronoi diagram, which is also called Voronoi tessellation, Voronoi decomposition, or Dirichlet tessellation, is a particular type of decomposition of a metric space, which is originally developed by Dirichlet and Voronoi. Voronoi diagrams are defined as followings;

Suppose that P = {p1, p2, p3, …. , pn} is the set of points on the plane. (Such point are called a site.)

V(pi) = { q| dist(pi,q) less than dist(pj,q) , j != i }

where, V(pi) is called the Voronoi cell for pi, and is the set of q which are closer to pi than any other sites.

According to the definition of Voronoi diagrams, a Voronoi edge is the perpendicular bisector between pi and q.

On the other hand, Delaunay triangulations are the dual graph of Voronoi diagrams for the same set P as the figure above shows.

For more detailed information and explanation of Voronoi diagrams and Delaunay triangulation, see websites, for example Wikipedia.

www.en.wikipedia.org/Voronoi_diagram
www.en.wikipedia.org/wiki/Delaunay_triangulation

According to the properties of Voronoi diagrams, there are various applications in many fields. For example, in geophysics and meteorology, the diagrams are used to analyze spatially distributed data including rainfall measurement. For anthropology, explanations of area in relation to influences of different cultures. For economists, the best distribution, model market. For ……… The list of applications are endless. Above all, one of the most famous applications is Snow’s Report on the Cholera outbreak in 1854. He used a Voronoi diagram to investigate distribution of the dead and area of assumed contaminated water.

Snow's map for Cholera

Meanwhile, what is the situations of Voronoi diagrams in design field including art, architecture, etc?? Due to nature-like and aesthetic outlooks, Voronoi diagrams are used by plenty of artists and architects. In fact, it is quite easy to find works in relation to the Voronoi tessellation. Their works are quite interesting and attractive. However, we might not be able to discover the ones which is associated with not only aesthetic composition of Voronoi diagrams, but also their mathematical properties that are applied to many researches in other fields as mentioned above. It may be because art or architecture is slightly different from other fields in terms of scientific researches. However, at the circumstances, beauty of scientific basis is probably necessary at least in architectural field according to the increases of environmental problems.

Biomimetic Butterflies : flight404

Yearbook pictures: Golan Levin

If so, how can the scientific beauty of Voronoi is achieved or applied into architectural field?? It is not easy for me to describe the exact examples or answers for the question, but there may be possibilities for me to find out the way of optimized area division at arbitrary point of façade in terms of internal space and external environmental influence, which is combined with sustainable design, especially energy efficiency. The idea is still developing and unfinished, but as soon as possible it is aimed to accomplish in near future.

Grotto: Aranda Lasch

AlgorithmicSpace: 000studio

Cellular Automata

Alan Turing’s “universal Turing machine” created in 1936 might be the essential invention of present computers. Afterward, John von Neumann had designed further developed self-replicating systems, which is well known as von Neumann Architecture, and the system is mostly similar to the present computers. In relation to such inventions, Cellular Automaton is formulated by von Neumann in 1940s. CA is composed of a regular grid of cells and simple rules which is related to time and neighbors of each cell. That is to say, the state of a cell at time t is determined by the state of its neighbors of the cell at time t-1. A cell has eight neighbors, and it means that the cell has 512 possible patterns at certain time.

In CA, Conway’s Game of Life is well-known version the system, which is produced by John Horton Conway in 1970. The system has just three simple rules as following;

1: Any dead cell with exactly three neighbors comes to life
2: Any live cell with two or three live neighbors lives, unchanged, to next generation.
3: Any live cell with fewer than two, or more than three live neighbors dies.

Concerned about such rules of the system, Conway’s Game of Life is associated with population ecological concept that a creature is not able to survive in a group with loneliness or overclouded.

At the present, not only Conway’s Game of Life, but also other several kinds of CA have been developed including Wolfram’s Rule 30, Cyclic Cellular Automaton, and so on. The followings are examples of CA.

Wolfram Rule 30

Spherical CA
Source from AD: Programming Culture Vol.76 Issue4

Symmetric Rabbits: Frank Buss
Source from AD: Collective Intelligence in Design Vol.76 Issue5

Processing

If you are an inexperienced person or a beginner of programming language including C, C++, Java, and so on, you might feel fear of touching these things. It is not actually quite easy to start to make something with complicated programming languages. And, people might think that they want to start to learn programming with simple, but abstract language, which can produce interesting outputs.

There is one interesting manageable programming language, called Processing. It is originally developed by the MIT Media Lab for those who are not given any education of programming, but keen on using them for their activities, for example artists, designers, etc. At present, Processing is widely used for introduction of programming at various universities and polytechnics, mainly departments of art. Furthermore, it is possible for people who have certain extend of skills of programming to make products of exceedingly high quality. Processing, that is to say, is a useful tool for many people. The address below is the website of Processing, and free download is available from the website. There are also several interesting works and links there.

http://www.processing.org/

The followings are fascinating as well as the website above.

www.benfry.com

This is the website of Ben Fry who is one of the main developers of Processing. He researches develops the ways to combine various different fields such as computer science, statistics, graphic design, and data visualization, and Valence or anemore is parts of his works.

www.reas.com

Casey Reas, the other main developer of Processing, also produces quite interesting art works as well as Ben Fry. Architectural Design magazine published his article and works in AD July/August 2006: Programming Culture, pp26-33

Some other interesting website related to Processing are followings. They are just parts of huge amount of works generated by Processing, and it is possible to find other materials and source codes from the internet.

http://www.levitated.net/

http://www.complexification.net/

http://www.mos-office.net/

L-systems

Lindenmayer systems, or L-systems for short, are formal grammar, which were originally introduced by Aristid Lindenmayer in 1968 as a thesis of the research which investigated the development of simple multicellular organisms. Afterward, the systems were applied to higher plants and plant organs. At the circumstances, L-systems are well known as the plant modeling systems explaining the plant structures and its development processes, and computations of the processes are frequently manipulated in the field of digital biology. Additionally, architectural field is also one of such fields using L-systems, which might be comparatively emergent subject in the absolutely long history of architecture.

The followings are some examples of digital designs using L-systems. The first one is Phyllotactics designed Alisa Andrasek, biothing, and the second work is scripted by Marc Fornes, who is one of the youngest and the most energetic architects in the field of architectural digital design.

Phyllotactics: AlisaAndrasek

source: www.biothing.org

Marc Fornes

source: www.theverymany.net

There are many other interesting architectural works in relation to L-systems, and such applications of L-systems to architectural design would be researched and developed much more in future as digital design goes father.

As far as concerned about the L-systems, how does it work in practical? Before explaining its details, it is necessary to understand its grammatical structure, which is generated by context-free L-systems, well known as OL-systems.

G = { V, ω, P }

where, V is the alphabet of the system, which is denoted as V* and V+. V* is the set of all words over V and V+ is the set of all nonempty words over V. ω is called the axiom or initiator defined by V+. P is a finite set of productions derived from V and V*, and additionally the set, (a,x) is determined by P is explained as a → x, where a is called the predecessor and x is called the successor.

If an OL-system is deterministic, which means that there is only one rule of a → x, OL-system is called as DOL-system. On the other hand, rules of a → x are in dependency on a probability, the system is a stochastic L-system. Furthermore, the systems are categorized in terms of more detailed elements. The book called the Algorithmic Beauty of Plants written by Przemslaw Prusinkiewicz and Aristid Lindenmayer contains more details.

The followings are parts of examples of L-systems, which are very simple samples.

Example 1: Algae

V: a, b

ω: a

P1: a → ab

P2: b → a

The sequences generated by the above system are as follows.

a

ab

aba

abaab

abaababa

…

source from the book: The Algorithmic Beauty of Plants

Example 2: Koch Curve (Turtle Interpretation of Strings)

V: F, +, -

ω: F

P: F → F+F-F-F+F

where, F means to draw forward, + means to turn left at 90 degrees, and – means turn right at 90 degrees. Turtle interpretation of strings is explained in particular in the Algorithmic Beauty of Plants noted above.

source from the book: The Algorithmic Beauty of Plants

The results of the system are shown as follows.

F

F+F-F-F+F

F+F-F-F+F+ F+F-F-F+F- F+F-F-F+F- F+F-F-F+F+ F+F-F-F+F

…

source from the book: The Algorithmic Beauty of Plants

Examples above are only simple elements of L-systems, and it is necessary to understand detailed parts of the systems in order to generate digital organisms or plants.