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Variation on a Cayley Tree

Variation on a Cayley Tree

Piece description from the artist

The Cayley tree is a mathematical object related to a Bethe Lattice (see the wikipedia article for an overview here: http://en.wikipedia.org/wiki/Bethe_lattice). It’s essentially a branched structure. Each node joining the branches in the “tree” has three branches emanating from it (think of it as a trunk that forks into two branches at the node). Each branch terminates at another node which also branches. A smooth plane has two dimensions and a smooth line has one dimension, but a Cayley tree has an intermediate dimensionality. This can be useful for certain types of calculations: where a fractal surface either better reflects the physics of the system, or where the symmetry of the Cayley tree simplifies the physics and/or math. In “Variation on a Cayley Tree” some liberties were taken with the strict branching geometry and topology of the mathematical object, in order to map it onto a form that actually resembles a tree. The drawing “Variation on a Cayley tree” is part of a series of drawings and paintings examining tree symbolism in nature, and in the world of scientific ideas.

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5.0" x 8.0"
ink on paper

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