Ming the Mechanic:
New Math

The NewsLog of Flemming Funch
 New Math2003-05-04 23:05
picture by Flemming Funch

Synergetic Earth News mentions this article about a new mathematical formula invented by a Belgian biologist, which apparently can generate a surprising range of natural shapes.
One simple equation can generate a vast diversity of natural shapes, a Belgian biologist has discovered. The Superformula, as its creator Johan Gielis has christened it, produces everything from simple triangles and pentagons, to stars, spirals and petals. ... The Superformula is a modified version of the equation for a circle1. Changing one term in the formula varies the proportions of the shape - moving from a round circle to a long and skinny ellipse. Changing another varies the axes of symmetry - shifting from a circle to triangle, square, pentagon and so on. Varying both proportion and symmetry together produces shapes with any number of sides, regular and irregular. It can also produce three-dimensional structures, and non-biological shapes such as snowflakes and crystals. "It's a new way of describing nature," says Gielis.
Now, where's the damn formula? Wolfram has a discussion of it here. Not that I really understand it. And it seems that Gielis has formed a company based on his formula.

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5 May 2003 @ 10:47 by craiglang : Deterministic and Transcendental
The first thing one really notices is that the forumla is a single valued, closed form function of one variable - the simplest possible form of function. The results are therefore deterministic, yet by varying the constants (m, n1, n2, a, b) they are also arbitrarily complex. A fascinating glimpse into the wonders of the mathematical world...  

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