Fractals appear in many places in biology and ecology, in society, in man-made artefacts. Yet the concept itself is quite new. Fractal phenomena existed for a long time before Benoit Mandelbrot formally investigated them as such. Amazingly, the Greeks, who did so much, do not seem to have had the notion of a fractal.
In the age of software, we can easily understand that fractals simply are the result of a function applied to its own output at different levels of scale. We know what that function is if we have written the software ourselves, but it might not be so easy to know what it might be if a fractal is detected in nature, say.
It seems that today we have instruments for observing all kinds of basically linear things at many different scales: microscopes, telescopes, oscilloscopes and so on. Yet, there is no good instrument for detecting self-similar phenomena that appear at multiple different orders of magnitude. For example, how could I look for fractals in the genome? In the organisation of my local community? What methods should I use to extract the process that generates the self-similarity?
We are very comfortable with thinking about linear quantities and smooth shapes, but applying linear methods to fractal phenomena will often miss the point. This is one of the essential points that we may take from Nassim Taleb’s Antifragile.
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