FOUR FORMS - a structural explanation

2011

All of my recent work, Passacaglia, and Tetras are constructed solely from combinations of the four triangular forms or tetrahedra: Alpha, Beta, Gamma and Delta. This operates similarly to the subliminal mathematics in music. It provides a formal cohesion and narrative for the work.

These specific tetrahedra combine in varying sets to build larger copies of themselves. For example 2 Betas, 1 Gamma and 4 Deltas can combine to build a larger Beta. Similarly, each tetrahedron contains substructures of smaller and smaller tetrahedrons, that develop almost fractally.

The tetrahedra have interesting and complex properties:

• They can be combined in patterns that fill 3D space without voids.

• These patterns are aperiodic. Unlike bricks, they cannot be assembled into a single, regular pattern that repeats. Instead they radiate out in varying angles and combinations.

• The ratios of the edges and the sizes of each tetrahedron are related by the Golden Mean.

These specific tetrahedra combine in varying sets to build larger copies of themselves. For example 2 Betas, 1 Gamma and 4 Deltas can combine to build a larger Beta. Similarly, each tetrahedron contains substructures of smaller and smaller tetrahedrons, that develop almost fractally.

The tetrahedra have interesting and complex properties:

• They can be combined in patterns that fill 3D space without voids.

• These patterns are aperiodic. Unlike bricks, they cannot be assembled into a single, regular pattern that repeats. Instead they radiate out in varying angles and combinations.

• The ratios of the edges and the sizes of each tetrahedron are related by the Golden Mean.