Tag Archives: differential geometry

Valency (video)

These are clips of how the particle systems described in previous posts move in space. It’s all very raw, but I wanted to get something out there. The larger structures suffer from convergence problems creating oscillations, twisting, foldings, and other … Continue reading

Posted in Computational Technique, Space and Geometry | Tagged , , | 7 Comments

Connecting the Dots With Differential Geometry

Particle-Based Structure Formation In order to build a complex and dynamic spatial system, there need be entities operating at multiple temporal and spatial scales.  As mentioned in the previous post, the extremes of the spatial scale are local and global … Continue reading

Posted in Computational Technique, Space and Geometry | Tagged , | 3 Comments

A Transversion Machine Redux

Thoughts on the Original Design The motivation for constructing a transversion-based spatial automaton was to construct a surface in 3D Euclidean space from as little local geometric information as possible.  It was the automaton’s role to expand the information into … Continue reading

Posted in Computational Composition, Computational Technique, Space and Geometry | Tagged , , , | 2 Comments

A Transversion-Based Machine for Curvature

Fundamental Forms One of the key properties of a manifold is its curvature.  For simple shapes such a sphere or a plane, curvature is constant, but for the most part it is a function dependent on position in the manifold. … Continue reading

Posted in Space and Geometry | Tagged , , , | Leave a comment