Fractal Spirituality-The Infinite Within Our Souls

Has known God,
the God who knows only four words.
And keeps repeating them, saying:
Come Dance with Me.”

How can a Mystery as large as the Universe find expression within the smallness of our souls? How can we tiny beings experience the Infinite? I found a new way to think about this question when I learned about fractal geometry. Fractals are never ending patterns, with self-similarity at all sizes.

Benoit Mandelbrot was the mathematician who first coined the word fractal, and brought to our attention the possibility of exploring the geometry of the natural world. Fractal comes from the word for broken, and Mandelbrot wanted to explore the rough shapes of nature. Traditional Euclidean geometry could not describe these shapes. Mandelbrot wrote: “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in straight lines.” Fractal geometry enables scientists to describe the world through complex mathematical formulas.

Mandelbrot Set by Wolfgang Beyer, Wikimedia Commons

Mandelbrot Set by Wolfgang Beyer, Wikimedia Commons

I am not a mathematician, but I was curious to see if I could make sense of the math. Perhaps you have heard of the most famous image associated with fractal geometry, what is called the Mandelbrot Set. It has a dark area that looks a bit like the shape of a bug, with a large round spot, and a small attached round spot. But the edge is what makes it fascinating. It is filled with beautiful complex curlicues that continue to be complex curlicues no matter how much the set is magnified. In fact, it continues through infinite magnification.  (For more images of magnification, see here.)

Mandelbrot Set Magnification by Wolfgang Beyer, Wikimedia Commons

Mandelbrot Set Magnification by Wolfgang Beyer, Wikimedia Commons

But “What is it?” I wondered.

If you have math anxieties, I promise you, I am only going to give a simple explanation with ten sentences. You are also welcome to skip the next paragraph.

A Mandelbrot Set is a diagram of a mathematical equation. The equation is: Z = Z2 + C. You insert a number into the equation, and the equation computes it to a new number. Then you start the equation all over again with the new number. Now here’s the interesting part—we don’t care about the answer. We care about how many times you can repeat the equation, with the number you started with. If you can repeat it only a limited amount of times, that number is part of the Mandelbrot set—and it becomes a black dot on your diagram, part of the black spot. If you could repeat it an infinite amount of times, that number is outside the Mandelbrot set. Depending on how quickly it gets to be infinite, it can be given a different color. Only computers can actually do all of these calculations, but they do them very well, and so we can see the images formed by the equation.

Okay, I’m done with the math part now. (I didn’t go into complex numbers or imaginary numbers, so my apologies to anyone who really knows about all of this. But for the rest of us, it is probably more than enough anyway.) The thing is, when Mandelbrot computed his formula, it created a picture filled with beautiful complex curlicues. And no matter how many times you magnify the picture, you will continue to see similar complex curlicues.

More tomorrow…



For those who would like more detail about the Mandelbrot Set, see the website Introduction to the Mandelbrot Set: A guide for people with little math experience by David Dewey.


3 thoughts on “Fractal Spirituality-The Infinite Within Our Souls

  1. Love this. I did my undergraduate work in mathematics – which I fell in love with because of the fractals. The beautiful mystery of patterns repeating themselves at scale and in unrelated contexts was a hint at making meaning of the complexity of the universe.

    Turns out I am a lot better at theology than I am at mathematics, but we figure these things out eventually. I look forward to your further thoughts on this topic.

  2. I have only been reading about your life journey for a couple of months, but find they ‘talk’ to my needs and experiences in a very special and meaningful way. I was very interested in your description of your meditative journey into emptiness. This week I intend to follow the steps you suggest to see what unfolds. Oddly enough, though I have very basic mathematical understanding, some years ago I became intrigued by fractal geometry and continue to be as if under a spell. I look forward to your posts on it.

  3. I LOVE FRACTALS! And I know only a tiny bit about them. I’m so excited to read your reflections on them. Keep ’em coming!

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