One of the first studies of fractals came from a surprising and weird phenomenon that occurs when you try to measure a coastline.
Fractal geometry is one of the most elegant and beautiful branches of mathematics.
You probably haven't thought of fractals since your high school geometry class, but there's a chance you've crossed paths with the otherworldly patterns recently. From trippy dorm room posters to the special effects in the blockbuster film"Doctor Strange," the endlessly recursive designs have become a cultural shorthand for awe and wonder.
Many shapes in nature have fractal-like properties. Crystals show the kind of repeating"self-similarity" that the Koch snowflake does; tree branches grow out into smaller and smaller versions of themselves; and lightning bolts follow fractal-like paths through the air. It turns out that measuring the length of a coastline depends on the length of the ruler you're using, or the resolution of the map or photo being measured. That is somewhat counterintuitive, since most distances we might measure day to day don't change with the length of the ruler used to find them.
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