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Wolfram Summer School


Maurice Martel

Summer School

Class of 2007


Maurice Martel graduated from Laval University in Quebec with a master’s degree in architecture. Characterized by the excellence of his academic profile and achievements, he won several awards and a prestigious grant among all Quebec schools of architecture. Martel has worked on eminent projects in the United States and Canada. He collaborated with several renowned European firms such as Zaha Hadid, Servo, NL Architects, and Veech Media Architecture. Martel also co-founded Open Form Architecture in 2005. The members of Open Form Architecture have collaborated with architects like Ramoisy Tremblay Architects since 2001. Open Form Architecture defines an architecture practice as a satellite studio wherein partners join together to work on projects, competitions and exhibitions from their studios in Montréal, Los Angeles and Rotterdam. Open Form Architecture seeks to define a new practice of contemporary architecture based on complex tools such as programming, generative algorithms, biomimetic software, and associative design in order to arrive at a practice wherein the formal investigations are endless open forms.

Project: Tractable Shape

What if a building could shape itself depending on the context where it is built! This statement might be hard to understand in a physical world, but let us assume, for instance, that it is a theoretical problem. In fact, a building always has to respond to certain constraints due to the context wherein it is inscribed. Indeed, streets, surrounding buildings, municipalities. rules and codes, topography, the program of the building (its use), etc. are the tip of the iceberg of what an architect has to deal with when he is designing a building.

My objective in the use of Mathematica is to explore the phenomenon of an accurate shape which could be remodeled according to divergent contexts where it is inserted. However, structure, space, and envelope all have to be connected to each other and react the same way. Thus, the answer would be to define a distorting outer shell which is linked with the inner structure and its inner space.

Concretely, I will initiate this problem by modifying the outer limits of any pattern or structured shape inside of some boundaries with the manipulation of a polygon with locators (this first attempt will be done in two dimensions). One of the problems is then to keep the intelligibility of shape organization inside of the limit even though it is irregular. It should then maintain its behavior and rearrange itself proportionally with the new shape of the shell.

I will then insert a cellular automaton with a random initial condition into those boundaries. They should therefore react or recalculate every time the boundary is changing. The tricky part in this is that I have to figure out how the cells that touch the limit are changing color whether they are inside or outside the limit. If the limit is moving inward, every cell outside will then turn white (0). If it is the opposite condition (the limit moves outward) the cellular automaton will recalculate by considering that its neighbor has been changed. This problem appears to never have been explicitly studied, so I will probably have to create a new function for that.

The third step would be to transpose this into three dimensions. It will then become more architectural.

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 9376138

My favorite cellular automaton is rule 9376138 because its shows a certain complexity, but then you can see a structure; and I think it’s quite architectural.

The code is Manipulate[ArrayPlot[CellularAutomaton[{a, {3, {3, 1, 3}}}, {{1}, 0}, {55, All}],Mesh -> True], {a, 0, 14348907, 1}]

Relevant Wolfram Blog Post

A New Kind of Building?