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Monthly Archives: March 2011
Transversion and the Torus
As a first test of the efficacy of the new Transversion Automaton design, I set it up to carve out a simple torus. Since a torus only has two loops whose product generates the surface, it’s easy to model simply … Continue reading
Posted in Computational Technique, Space and Geometry
Tagged geometric algebra, torus, transversion
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Hyperbolic Tilings Again
I’m revisiting a lot of the techniques I’ve implemented for working with hyperbolic geometry as I’m rebuilding the Transversion Automaton in order to make the simpler and clearer. The most basic structure that underlies the topology of the surfaces generated … Continue reading
Posted in Space and Geometry
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A Transversion Machine Redux
Thoughts on the Original Design The motivation for constructing a transversionbased 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
Hyperbolic Translations
One of the crucial issues in the construction of the implementation of the transversion automaton is how it interpolate its geometric relationships (transversions and rigid body motions) through space to generate a surface in 3D. The input data is pentagonal … Continue reading