Experiments in Amorphous Geometry

Amorphous computing is a recently introduced paradigm that favours geometrical configurations. Physically, an amorphous computer is based on an irregular and error-prone distribution of a large number of simple processing components; this is well-suited for handling spatial structures. It has come to our attention that the venerable discipline of computational geometry could benefit from the amorphous computing approach. It seemed natural to refer to this approach as amorphous geometry. Although at this stage our exploration of this concept is fairly modest, we feel that our experiments are sufficiently convincing and merit further study. Investigating amorphous geometry should show that amorphous computing can deal with various classes of problems from computational geometry and may eventually expand the field considerably while resulting in useful applications. Especially our preliminary results concerning the triangulation problem are of importance since it is very representative case in computational geometry: it covers a whole family of problems.