The Mandelbrot Set
In nature there are patterns that repeat, sometimes at many different scales within the same structure. Look at a seashell or a fern frond and you can see evidence of this.
I’m not any kind of mathematician, math scientist or math student, so I’m very limited in how much I can intelligently write on this topic. And it follows that this will be a pretty brief post.
When Mandelbrot first expressed this set of numbers mathematically in the 1970s, there weren’t a lot of available tools to graph this set out accurately. Most computers of that time had very limited monitor screen displays, if they had monitors at all…most output then was printed on paper. This had to be frustrating to Mandelbrot and his associates. But what had to be even more frustrating (albeit amusing today to read about), is that when he finally had this set of self-repeating patterns plotted out on large-format paper, the plotter technicians had taken it upon themselves to “clean up” and erase the small intricate spirals and patterns dotting the edges of the Mandelbrot Set, assuming they were dirt, ink traces, or other anomalies left mistakenly by the plotter heads.
Today there are several online tools to explore, zoom in/out, and otherwise experience at trillion-x scale the miniscule self-repeating (and I daresay beautiful) patterns of the Mandelbrot Set. Rather than further reveal just how limited my math understanding is, I will encourage people to look some of them up online and see for themselves.
Here endeth the lesson on the Mandelbrot Set.
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