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
About Me

Who is Indigo Boy?

When I was about 12 years old (1950) I began visiting the Carnegie Library (Hastings Nebraska) with my brother Joe. Joe was a bit more than one year younger than me, but he had already discovered the music room of the library. We would sit in the room and listen to the classical music with earphones. The library had a wonderful collection of 78rpm sets of the best classical music. Here I was introduced to Beethoven, Ravel, Sibelius, Mozart, Back, Bizet and many other composers. This was one of those wonderful experiences that has been a blessing my entire life.
One afternoon after school in the spring of 1951 Joe and I had been listening to Sibelius' 2nd symphony, me for the first time. The "triumph" of the symphony had put me in a very thoughtful mood and I got up and started looking through the book shelves adjoining the music room. I had been interested in Chemistry, as I had put much energy and all the money I could lay my hands on into developing a small lab in the back porch of my parents tiny house. I looked through titles of chemistry books until I came to one called "The Chemistry of Organic Compounds" by James B. Conant. As I thumbed through the book I was taken by the chemical structures on almost every page and the occasional apparatus diagram. On page 510 I came to a discussion of the chemistry of the Natural dye indigo and its synthesis, shown by the reaction sequence above.
I became completely fascinated with indigo, its chemistry according to Conant and proceeded to read all about it. The history of this ancient plant substance is extremely interesting as it is the deep blue dye used by the North African Arabs to dye clothing, and still today is the deep blue dye used to dye denim jeans and is responsible for the characteristic odor of new dark blue jeans. It was an ancient item of Indian commerce which played an important role in Gandhi's freeing of India from British rule as the artificial synthesis of indigo had been used by Britain to "rob" the Indian population of one of its household industries. I wrote a paper for my eight grade English class on the History and Chemistry of Indigo and received a solid A for it from Sister Mathias (Joe and I had the same teacher since the 7th and 8th grades classes were small.)
The structure of indigo was deeply fascinating and I began a study of its analog dyes like tyrian purple. I actually purchased samples of a variety of dyes from many different chemical companies including Tyrian Purple and Chrome Yellow. This led me to eventually study Organic Chemistry in college and eventually obtain a PhD in Organic Chemistry from Vanderbilt University. I learned to do many experiments in Organic Chemistry in my own lab. I did syntheses like aspirin, acetanilide, tribromoaniline, trinitrotoluene and even a small amount of nitroglycerin which started a small fire in the garage in back of the house.
But the more I dealt with the history and chemistry of indigo the more interesting it became. Eventually I saw the possibility of a new type of polymer in the indigo chemistry. That thought led me to a project and a prize the Science Fair in Nebraska of 1957(Westinghouse Science Talent Search). The following post will be a description of that project and its important meaning.