Snow and ice comes to mind when the word “fractal” is
mentioned. But of course, they are indeed examples of fractals. What a fractal
is, is that it’s a shape or an on-going complex pattern that is self-similar
across different scales. Some of well-known fractals include the Sierpinski
triangle, the Mandelbrot set, the Koch snowflake, the Julia set, and the
Apollonian gasket. Some examples of fractals occurring in nature are river
networks, frost crystals, coastlines, Mountain Goat horns, and patterns on tree
leaves.
One of my favorite fractals is definitely the Apollonian
gasket, named after the Greek mathematician, Apollonius of Perga. It seems
quite simple, but it’s maths. The fractal is generated from triples of circles,
where each of them is tangent to the other two. And the Apollonian network is a
graph derived from finite subsets of the Apollonian gasket.
#exploremaths
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