Sponge

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date: 2012, 1st semester
course: (Architecture major) Architectural Design Studio 1-1
interval: half-semester (mid term)

Sketch

Diagram

There are several ways to explain Voronoi diagrams, but the following explanation is quite intuitive in that it captures the principle that the structure of a sponge is formed by multiple cells simultaneously growing and occupying space.

Start by scattering several points on a plane, and draw circles centered at each point with continuously increasing radii. At the moment when a growing circle meets another circle, stop the growth at that point of intersection.

The figures above briefly illustrates the process.

$V_k$ is defined by Voronoi space based on points $P_k$ within $n$ dimensional Euclid space. This logic expressed in the language of mathematics states that a Voronoi space is a set of points that are closer to a particular reference point than to any other reference points. The figure describes the Voronoi space inside cubic frame, where $n=3$ and $m=20$.

From a geometric perspective, when constructing a Voronoi foam for arbitrarily given points in three-dimensional space, each cell is composed of an average of 14 faces, and each face is composed of an average of 5 edges.

Human-scale Study

Space Generation

Void

Human-scale Space

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