How does the concept of a fractal differ from that of a traditional geometric shape
In: Mathematics
The informal understanding of a fractal is that it’s a shape that is self-similar. That if you zoom in, you see shapes that look the same as the whole thing, and this zooming can be done infinitely.
However, a mathematical definition of a fractal is any shape that has *a fractal ‘dimension’ that exceeds its “topological dimension”* (among other definitions – there’s no unified definition of a fractal, and there are multiple different fractal dimensions), where this these dimensions are calculated by an extension of concepts like length, area or volume that we are familiar with. The definitions involved can get quite involved and deal with things relating to covering the shape so I’ll avoid detailing them here (you can look them up). It also often involves non-integer dimensions (the Sierpinski triangle has fractal dimension of about 1.585). It just so happens that many of the famous fractals do exhibit some level of self-similarity.
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