Each cabin has a simple inner hierarchy: cabin, facades, segments (of facade), pieces of materials. The geometrical arrangement of objects in the lower level becomes the texture for the higher level objects. Thus the higher level objects become the media for the information in the lower level.

Besides, A set of rules are programmed to select the resulting geometries as useful volumes of architecture. The distributions of areas on each floor (built by slicing the solid volume), the complexity of the boundaries of the floors and the compactness of the floor shapes are among the main concerns. Through this method, a loose but rich link between  the 3-d articulations and the 2-d shapes of floors are established.

Programmed in Java

June 2012

Two family of models are built for architecture, one for the 3-d form of the building, another for the floor plans. The two models are often loosely coupled, in other words, the two are closely related to each other rather than be determined by the other. In this experiment, this relationship is established through a flexible communication channel.

Two members of  3-d form family:

1. Perlin: smooth surfaces constructed from a scalar field of Perlin noise.

2. Cubes: geometry resulted from boolean operation of three cubes.

Two members of floor plan family:

1. Central corridor: creates an horizontal (along the long side of the floor) corridor around the center of the floor.

2. Voronoi: arranges the corridor and the rooms based on Voronoi tessellation of the floor area.

Programmed in Java

April 2012

A pair of grids and a pair of volumes are employed to generate architectural forms. This experiment commences with two groups generators, each group consists of a grid and a volume which are twisted with each other. Inside each group, the floors are generated on the grid and within the volume.

An optimization process is to arrange positions (in vertical direction) of floors such that the total area of floors are maximum and all floors have a proper height. Since the floors are associated with both the grid and the twisted volume, generating all floors without conflict by rule-based method is not available. Instead, an optimization process starting from random initialization is more reasonable in this situation. Besides, such process is better at generating alternative solutions than rule-based methods. Both “generate and test” and simulated annealing are tried for optimization. The convergence speed of the methods are similar in this experiment, both takes hundreds to one thousand iterations to get satisfying results.

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The research is partially inspired by Colin Rowe’s celebrating paper (1947) “The mathematics of the Ideal Villa”. The paper coined the so called “ABABA” rhythm of the grid underlying both Le Corbusier and Palladio’s villa design. The proportion of grid is 2:1:2:1:2 in one direction, other direction has factors of 1.5 and 2(1.5+0.5). A similar grid plays an essential role in both designs. However, this paper might be misleading that the two designs are dominated by the grid. Quite obviously, the model of volume also plays an essential role in both designs, Palladio’s villa employed symmetry volumes while Le Corbusier used subtraction of volumes.  If we regard the grid and the volume in Malcontenat and Garches are well correlated, some deconstructivism architects strive to evoke the conflicts between the two model. Re-organizing these conflicts leads to meaningful compositions.

The experiment arranges rooms and functional units (e.g. entrance hall, terrace, stair case) on a grid and within a single cuboid volume. The grid adopts the rhythm of the grid in Villa Stein (Rowe 1947). The volume is divided into several layers by a fixed interval(equal to the height of the floor). These layers of volumes are further subdivided into smaller volumes by the underlying grid. The functional units occupy the subdivided volumes(one unit could occupy many units), as a result, the boundaries of the units are aligned with the gird and all the units are within the original cuboid volume.

The experiment defines four functional units: an two-layer high entrance hall, a stair case, a two-layer high conference room and a terrace. There units are randomly generated under certain constraints, for example, the entrance hall have to be in the first layer and be directly accessible for outside of the volume. The area of the units are also constrained.

An optimization process is to improve the composition of functional units. The concerns include:

1. The position of the stair case should facilitate the circulation.

2. Avoid the collisions between the functional units.

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Programmed in Java

September 2010

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The project of Himmelstadt asks if self-organizing system could be systematically regulated according to the user’s preference for global behavior. Self-organizing has benn appreciated by architects and urban planners for its richness in the emerged global behaviors, however, design and self-organizing is contradict in principle:

the former approach often assumes a methodical step-by-step planning process with predictable outcomes, whereas the later involves nondeterministic spontaneous dynamics with emergent features. - Prokopenko 2008

This experiment is to evolve the rules of Cellular Automata (CA) according to the observer’s preference for global patterns. A CA with eight neighbors is employed, the state of a cell in the next iteration is determined by the current states of the 3×3 grid around it. Thus, the updating rules is a function that has nine boolean inputs and one boolean output. The task is to derive a specific function which leads to a preferred global behavior. Based on the interface, the user could select one particular CA to see an animation of the evolving process. By these images or animations, the user could input his preferences (give high scores to several favourite ones ). Then the computer would create a new generation of CAs by reproducing, mutating and crossing the preferred ones. The procedure is very similar to genetic algorithm, in which the new generation always has new variations and probabilistically moves towards certain direction imposed by the selection.

At the final stage, the selected CA is used to simulate the development of a city district. There are two aspects which are valuable for architects or planners. One is about the form which might contain interesting shapes or special topological structures; the other is about the stability of the dynamical system: some CAs would convergence to a certain pattern (towards equilibrium) even with different initial states; by contrast some others would have very different results even with similar initial states.

Programmed in Processing

CAAD/ETH MAS module with Brian

January 2010

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Evolution of Cellular Automata based on user preference

This experiment employs three distinct models for generating floor plans: a set of shapes, graph and polygons. From a viewpoint of architecture, three models fall into two categories: the model for the solids(the wall) and the model for the rooms. The set of shapes are employed to represent the solids; the graph and the polygons are used to represent the rooms.

The set of shapes include simple shapes like “T” shapes, “+” shapes, circles, quadrangles and so on. A set of these shapes constitutes a wall system that make partitions of spaces.

The graph is employed to represent the topology of the rooms. The method is very similar to Hillier’s (1986) formulation. Every node denotes a room, a link between two rooms means that two rooms have to be next to each other and be accessible from each other. The topological information of the rooms are inputs of the program.

The polygon is the model to represent each room. The main concerns in this model is how good(or bad) is a polygon as a room? First of all, the area of the polygon is obviously an important criteria. Beside, the rectangle as the “standard” shape of the room is employed to measure how good(or bad) is the shape of the polygon. The larger the overlap area between the rectangle and the polygon, the better the polygon is.

The process to generate the floor plans with the three models include the following steps:

1. make a composition with the predefined shapes, detect all closed regions as potential rooms.

2. Find a set of regions that satisfies the predefined topology of rooms by graph matching algorithm.

3. Change all the shapes gradually to improve the areas of the selected regions. The topology between these regions are kept still.

4. Change all the shapes gradually to improve the shape of every selected region. The topology between these regions are kept still.

Programmed in Java

September 2011

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