Gertsch Group

Institute of Biochemistry and Molecular Medicine, University of Bern, Switzerland

Beauty in mathematics, beauty in nature

Beauty in mathematics, beauty in nature
Jurg Gertsch - Wed Dec 30, 2009 @ 04:18AM
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Mandelbrot 3D

What looks like the surface electron micrograph image of some material is in fact the improved Mandelbrot fractal set of points in the plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded, which is a function f defined on some set X with real or complex values, if the set of its values is bounded. In other words, there exists a real number M < ∞ such that for all x in X. Benoit B Mandelbrot is a French American mathematician known as the father of fractal geometry. If you are interested to know whether fractals are at all relevant to nature and your life have a look at this site called hunting the hidden dimension (you can see the movies only within the USA).

Daniel White from Bedford England has managed to unravel the 3D Mandelbulb and it looks like a natural 3D structure - I wonder whether we are getting closer to apply this sort of fractal geometry to 3D imaging of molecular surfaces. Instead of stopping at the resolution of light or sticking to individual crystal structures at Angstrom resoultion we may be able to walk through cellular universes. How wonderful it would be to explore the surface of a cell in the Mandelbulb world - is this what nature portrays or is it more a model of our own longing for beauty in nature? What sounds like science fiction has become one step closer to reality.

Daniel Whites Mandelbulb

If you think about it, maybe we are only able to see and portray what nature has inbuilt already. We discover and rediscover what has been there for ever. This is nicely illustrated by the story published in Science where the maths student Peter Lu discovered that in ancient Islam the Penrose tile pattern was already known, at least empirically - a good read which makes you ask whether Roger Penrose 1974 had described something as new, which was in fact already in use for centuries. If Penrose would have had some classes in the history of art Lu would never have got his paper published ...

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