The Houston City is confronted with a paradox where on the one hand, it is expanding with a dramatic speed. However, on the other hand, it is still lacking of appropriate affordable housing because of the low density. So this project is focusing on the problem of density and affordability of Houston housing. By defination, density means how much the building fills a block, which could be translated from a mathematical approach. My proposal start with a research of the space-filling curve, which is a continuous curve that can be subdivided to infill the whole unit square. Because of the continuity nature of the curve, the housing community achieves both high density and a balance between public and private.

The project adopts the Space-Filling curve as an architectural language for the occupation of any given block. Through the translation process, the initially abstract curve is translated into vivid and active dwelling spaces. At the same time, it creates an ambigious relationship between inside and outside.