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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