Fractals

Did you know that it’s technically impossible to capture a perfectly defined measurement of the perimeter of our coastlines?

As you know, coastlines across the world range from smooth beaches to rugged and rocky terrain. Imagine stopping time and taking an aerial picture of the coast nearest to you, with, say, a resolution of 5×5 km. Got the picture in your head? Whatever coastline you chose, the perimeter of that coastline will have jagged features with scales that range from kilometers to tiny micro-meters. How do you measure this?

Let’s start with, for example, a certain section of the Oregon coastline that we want to measure with a yardstick. Once we’re done (after probably months of work) let’s compare that measurement to a measurement of the same perimeter with the diameter of a penny (~19mm, and probably a lifetime or more of measuring). The total length of the measurements would be drastically different. The smaller your scale, the larger the total perimeter of your coastline… literally to infinity.

Benoit Mandelbrot, a famous mathematician, after discovering this phenomenon, said, “[The world’s] coastline length turns out to be an elusive notion that slips between the fingers of those who want to grasp it.”1

Our world is so incredibly complex.

  1. https://archive.org/details/fractalgeometryo00beno/page/25/mode/2up

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