WHAT IS THE SIERPINSKI?
Waclaw Sierpinski was a mathematitian of the early twentieth century who, in 1916, published the geometric and fractal result of dividing an equilateral triangle into four triangles with sides 1/2 the sides of the original triangle with three sharing one each of the apices of the original. Each of the apex sharing triangles are again subdivided in the same way many times in succession. The final geometric pattern is a fractal called the Sierpinski Triangle or The Sierpinski Gasket. This geometric device lay fallow until late in the 20th century when it became a method of introduction to Fractal Mathematics and Chaos Theory. It has been demonstrated that the Sierpinski Gasket can be generated via the Chaos Game referred to below. The Chaos game generates the gasket by application of random choice and one strict rule to the indication of points in a beginning equilaateral triangular base.
The Sierpinski Gasket and the Chaos Game caught my attention in about 1983 when as an Organic Chemist I was responsible for the synthesis of novel drugs and agricultural chemicals. I had been fairly successful at the discovery of novel ag chemicals using a simple analog/homolog method of choosing synthetic targets. However in a few years I learned that this method would run out of gas very soon. I began looking for a method of choosing targets for drug and ag chemical synthesis using the same principle, i.e. by interaction of random occurances (steps in a random walk through a defined structural matrix) and the fundamental expression of Organic Chemical Transformation (strict rule). My group of synthetic chemists and myself had a bit of success using random walks through matrices defined by the property descriptors of chemical structures. While searching the math literature for new methods of applying the random/law principle I ran accross a description of the production of the Sierpinski Triangle by a method defined by a random choice of direction and a rigid rule of distance. I tried this on triangles, squares, pentagons and figures up to tweny sides. It always worked to give a geometric figure analogous the Sierpinski's Triangle. (I used a mac program written by my collegue Mike Miller, a fellow organic chemist.) I invented several methods for identifying synthetic targets for biological activity, but to my knowledge none of these have been applied beyond multiple synthesis. I have retired from the laboratory and my group disbanded to retirement and other endeavers. However, the understandings that I gained in these researches have provided a new means to understanding my own life and the "creation" of our world by analogous processes.
It was quite clear by that time that the evolution of life has been and is a product of the interaction of random occurances and the fudamental laws of physics and chemistry. It now occurs to me that evolution can be described in the same terms that produce the above geometric gaskets and figures. It has also occurred to me that processes of this sort may be applicable to understanding how the brain "works".

References: Larry Riddle and references to William McWorter at ecademy.agnesscott.edu

Alexander Bogomolny at cut-the-knot.org

Cynthia Lanius at math.rice.edu/~lanius/fractals/

The Chaos Game at mathworld.wolfram.com/ChaosGame.html
posted by Dad Brannigan at 11:15 AM 0 comments
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