Trying to push the boundaries

If you search up images of fractals, you see what hippies are into. But you also see some cool patterns that are pleasing to the eye. It turns out DNA is really like fractal seeds–using concepts of iteration and recursion–and so all of life as we know it on Earth is much like a fractal pattern too. Pretty cool. That’s probably why fractals are so pleasing on the eye. It would suck to look around at the world around us and have it be ugly. Compare Julia sets with ferns, as a good example.

Anyway, fractals are also fascinating because you can zoom in and zoom out and yet always see the same amount of complexity. You can probably search up some animated fractal .gif files that zoom in. Try the Mandelbrot set. That’s a good one for that. You keep zooming in, and you keep seeing the same pattern getting repeated. Pretty cool. (It’s like a heat map of how quickly complex numbers approach infinity when you keep squaring them.)

But notice this: The animated gifs don’t zoom in and out on areas where there is no clear pattern. It’s just the pattern that’s the most interesting. With fractals like the Mandelbrot set, the pattern is actually just the borders between regions of space. As you zoom in on the borders, they stay interesting.

It’s the borders where the excitement happens. The boundaries. That’s what people care about. Like the boundaries between land and sea. Tide pools are brimming with life. The boundaries between earth and sky. The boundaries between the chorus, the verse, the bridge, and the solo. The beginning of the song, and the end. The boundary of a black hole, or basketball hoop, or a nation. The boundary between inside your body and outside your body. The boundary between where relativity and quantum mechanics matter more. The boundary between the performer and the audience. The boundary between control and chaos. The boundary between love and hate. The boundary between being full and being sick. The boundary between truth and fiction. The boundary between repetition and redundancy.

I think boundaries really matter. Play with them. Explore them.

4 thoughts on “Trying to push the boundaries”

  1. Interesting thinking about boundaries. Boundaries are also about change. Change is always more interesting than something that remains the same. A boundary is where one thing becomes another thing. And “Those Magic Changes” are what music is all about.

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