http://www.nexusjournal.com/96/emmer.html

from that page:

Architecture and Mathematics:
Soap Bubbles and Soap Films

Michele Emmer, Professor of Mathematics
Universit? di Roma "La Sapienza," Rome
and Universit? "Ca' Foscari," Venice

"I hope that none of you are yet tired of playing with bubbles, because, as I hope we shall see, there is more in a common bubble than those who have only played with them generally imagine." Charles V. Boys

When Joseph Plateau published his treatise on soap bubbles and film in 1873, soap bubbles already had their own place in literature and art. Plateau's problem consists in taking a generic curve in three-space and finding a surface with the least possible area bounded by that curve. The empirical solution may be obtained by dipping a tridimensional model of the curve into soapy water, resulting in a form called a minimal surface. When a soap bubble is blown, the soapy surface stretches; when blowing ceases, the film tends toward equilibrium. The sphere presents the least exterior surface area of all surfaces containing the same volume of air.

The isoperimetric property refers to the fact that the circumference encloses the largest surface area. It is reasonable to suppose that people of ancient times in charge of founding a town were aware of the isoperimetric property, at least empirically: A town wall of the least possible length containing the largest area had to be circular. The circular plan is more prevalent in some periods of history than in others. C.N. Ledoux presented a circular plan for a town, the form as "pure as the one the Sun describes in its movement."

Like the circle, the sphere also appears in architecture. Ledoux planned a spherical house. His contemporary, Boull?I, used the sphere in the cenotaph of Newton. The hemispherical igloos of the Eskimos solve the problem of a structure based on a plane with the greatest possible volume for the same external surface.
Frei Otto used soap film models to design his tensile-structures. He developed a technique to obtain a precise photogrammetric evaluation of soap film models and another method to simulate peaks in a membrane of soap films. Otto's Institute of Architecture, Stuttgart, was built along the lines of such a model.

H.A. Schwarz solved Plateau's problem for a non-plane boundary by developing the periodic minimal surface. Infinite periodic minimal surfaces, combinations of saddle polygons or surfaces, are more stable. Such a surface has been adapted as a play sculpture in the Brooklyn Museum, where children can actually enter into the labyrinthic structure of periodic minimal surfaces.



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MYNOTE:
"The empirical solution may be obtained by dipping a tridimensional model of the curve into soapy water, resulting in a form called a minimal surface. When a soap bubble is blown, the soapy surface stretches; when blowing ceases, the film tends toward equilibrium. The sphere presents the least exterior surface area of all surfaces containing the same volume of air."
is this the key to get centroidal cells?

or is it with a formula to get center of mass using density function?

2001 classical/nonclassical computation http://architecture.mit.edu/descomp/works/Classical%2BNonclassical_Computation.pdf
terry knight and george stiny

download to pda

from that page

note: free form EIFORM by kristina shea (shape grammar and shape annealing method)

abstract

computers have come to play an important role in architectural practice. nonetheless, the promise of computation as a creative partner in practice, and a means to better understand and support the design process has yet to be realized. this article considers aspects of computation, and alternative ways that these have been approached in order to make computation useful in architecture and other areas of spatial design.

shape grammar genetic algorithm http://architecture.mit.edu/descomp/works/SGGA0502.pdf

consider non linearity... from a very linear grammar

form generator: computer game SPLINE SURFING

http://www.blobworld.com/hyperbody/txt/development.php

from that page

This is the report of the development of the 3d multi-user experience we, the auhors [1] , have been researching and developing this game from january to june 2003 for the Hyperbody research group[2] at TUD [3] , The Netherlands.

Our aim for this research was not to create a perfectly working form generator, neither did we try to create an environment that would specifically suited different expertises. We did try do make a game that enables muliple users to communicate and think about form, or architecture.

The actual release of the game, although it is a result of monts of research and development, is in fact the start of the research process. We hope this idea, of the software, will be prolonged and researched further in order to become a more mature designing tool.

We would like to acknowledge the help of our tutor, Oscar Rommens, the entire Hyperbody group and everyone involved in the process: Hans Hubers, prof. Kas Oosterhuis, Christian Friedrich, Misja van Veen and Walter Hop.

the authors are :
Marcus Buijtenweg, TU Delft bk no, m.buijtenweg@bk.tudelft.nl
Chris Kievid, TU Delft bk no, c.kievid@bk.tudelft.nl
Thijs Leydens, TU Delft bk515160, f.m.i.leijdens@bk.tudelft.nl

need to design 3 - 4 coding experiments to work on from now till xmas holies.

will start with last article (25 aug) and interpret that to my project.