Sierpinski's Triangle is made by pulling out the middle quarter of an equillateral triangle and, then, replicating that process with the triangles that remain. This rendering of it lifted off the net is a variant that doesn't quite work but that's a mathematical matter ... not to worry. The point of this fractal, as it is called, and others is that no matter how many "generations" you go into the process, the entire process is represented.
I knew Warclaw Sierepinski and his sidekick in developing Topology, Kazimierz Kuratowski, in the late 1960's/early 1970's. They had worked mostly from the 1920's to make Poland and its Academies of Science centers for the study of a specific type of Mathematics. S & K were young, then and full of their "unfolding processes." The French said that such national specialization would fail ... the French were wrong and those young men and a third, Janiciewski, who died in one of the Wars that took many young men's lives between the Great Wars played out their parts.
I thought of these Fractals last night ... as a denizen of the Fourth Quarter, I watched one of my younger grandchildren having already developed her own specific charachter. One of the younger ones, still not quite 10, was doing some performance art ... pretending in an improvised skit that the few drops of wine she had imbibed had changed her character. K intends to be an actress. Her older sister will be a writer. Even us Last Quarter types can recall when we were taking form ... at least our taking on the first of a number of forms that constituted the first Quarters of our performance arts.
And the beat goes on.
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