Tractable Shape I
by Maurice Martel
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’s 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 inscribe. 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 of that 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 fist attempt will be done in two dimensions). One of the interests is then to keep an intelligibility of a 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 have then to 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 touches the limit are changing color whether they are inside or outside the limit. If the limit is moving inward, every cells outside will then turn white (0). If it is the opposite condition (the limit moves outward) the Cellular Automaton will recalculate by taking in consideration 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 finally, to transpose this in three dimensions. It will then become more architectural.