New Geometry - extract from "The Shadow of the Cobweb."

A new geometry... 

March 1994 brought an article in New Scientist magazine about something called symplectic geometry, one ingredient of chaos theory. 'Symplectic' just means 'complex', but its mathematical associations are those of the complex numbers, in which minus one has a square root. In symplectic space a line is always at right angles to itself. Symplectic geometry includes velocities as well as positions, it is a geometry of motion. Well, he needed a new geometry, and since this one was on offer... He entered some sample formulas into his computer, trying to use symplectic geometry to model the motion of individuals in crowds. Suddenly, on the screen, in vivid colour, growing before his eyes, were the most striking, mysterious, and downright beautiful images that he'd ever seen. There were hundreds of them, thousands, millions. Every new 'seed' number that he fed his computer produced a new and different image.

For the full story by Ian Stewart - click here.

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