Fractals
The term fractal, coined by Mandelbrot, means ‘to break apart’ in Latin, and is meant to be held opposed to ‘algebra’, meaning ‘to bring together’ in Arabic. It seems, as they were originally conceived, that these two things are opposites.
Nevertheless, there are a number of connections that one can make between these two subjects, even if one doesn’t really know that much about either.
Symmetries
When we think of highly symmetric objects, might think of a circle, like this:
TODO: Add picture/interactive with circle.
You probably don’t think of something that looks like this:
TODO: Add a picture of a fractal.
When we say that a circle is symmetric, we mean that every pair of points looks the same. Put another way, for any pair of poitns, we can rotate the circle so that one point gets rotated on top of the other one. I think this is very neat for our understanding because it involves
The fractal though has a somewhat weaker symmetry property: