What are fractals? Fractals are technically geometric structures with a fractional dimension, for example 2.3. To understand what I just wrote, however, I'll give you an example: suppose you are told to trace a straight line. We know from elementary school that straight lines are just an infinite set of points lying in one dimension, and a straight line itself is therefore infinite.

Can you actually draw a straight line? No, but you can possibly draw a segment! A segment is an infinite set of points delimited by two extreme points. If for a straight line you need a whole dimension to trace it all, for a segment you will certainly need less than that!

In other words, you will need a fraction between 0 and 1 to trace it: therefore a segment constitutes a very simple, yet fractal, geometry! Can you predict, using the equation of a straight line, y = a * x + b, all possible segments that lie on a single dimension? Yes, but such an equation would generate an infinite, uncountable, uncomputable and therefore inherently unorderable set of values for the coordinates of the segment extremes.

We can now confidently state that nature seems fractal, but is that truly so? One may argue that the answer to this question has more to do with philosophy than physics, and in a way that would be correct. But what if fractals are just an emergent property our innate inability to grasp infinity?