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3D Lissajous Curves 
Strange Attractors 
Minimal Surfaces 





Minimal SurfacesThe geometry of anticlastic curvature is directly related to nonplanar minimal surfaces.Minimal surfaces occur naturally when a soap film spans a nonplanar threedimensional boundary. The surface tension seeks to minimise the energy required for maintaining itself and thus minimises the surface area. The mathematical interest is based on the special topological properties of such surfaces, and partially their economic elegance. I often found the boundaries of the mathematically rendered minimal surfaces to be rather restrictive and contrived, artificial  for they are still tied to x  y  z .. . and not an iteration  which is timebased and has a much more relaxed sense of origin (0,0,0), by referring back to the previous point rather than the orthogonal axes. .. (excuse this simplification  please send me an email if you can explain it . . .) ........ a thought on 'reference points' . . .I found that most minimal surface definitions are either simple and easily visualised without the computer, or very complex to the point where their mathematical definition is beyond my scope of understanding.The metaphor in this is that minimal, anticlastic surfaces embody the 'negative' curvature of hyperbolic space, which is a NonEuclidean space, and is also the complementary principle to spherical form, which is the basis of 'volume'. The anticlastic surfaces occur in transitional phases, and are more open to change than the selfenclosed sphere. Similarly, the transitional sections, between attractors, in a dynamic diagram (phase portrait) are often such saddle shapes, where the movement of flow goes up in one plane, and down in the perpendicular plane. As such they could imply an opportunity for change, open to outside impressions but also indecision.Heikki Seppä (an inspired silversmith) also pointed out that it is those spaces between things/solids which we easily overlook.... 

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