What’s this got to do with anything?

Fractality, or self similarity, is one way to think about why fluctuations get really big.

Around the critical point, there is a statistical self similarity. This is a quick way of saying that, as you zoom in or out, statistical quantities like averages and standard deviations basically stay the same, except for a change in overall size.

This connects really small changes (small scale) with much larger scales. And this is how fluctuations grow.

In a lot of the fractal animations, we saw some big shape getting finer and finer details, and these fine details all had the same original shape. But think about going in the opposite direction. If there’s a small fluctuation, it gets replicated (reproduced) at the next larger scale. This reproduction gets reproduced again, and the process repeats over and over and over again. So the fluctuation is like a fractal growing from small to big instead of big to small.

Fractality is then the magnifying glass that is at the root of what made fluctuations matter – and hence why critical opalescence occurs.

Why is there fractality?

Good question! Think about it....