Here’s a lovely talk by the guy who discovered them.
One thing he discovered is that if you have a coastline (like, say, Britain’s) and you measure it using a ruler say a mile long you might get a result that is about 11,000 miles. If you use a shorter ruler, say a foot long, you will measure more of the ins and outs of the coastline and you will get a bigger answer. If you have a very short ruler (say one atom long) you would measure the ins and outs of every atom along the way and the length would effectively be ‘infinite’.
The same applies to “what is the surface area of my lungs?” — it depends how long your ruler is.
And the most important insight? It comes at the end.
That all the complexity of the ‘Mandlebrot set’ (in the picture above-right) is created from an incredibly simple formula that has only two parts.
As he says it in words, “Bottomless wonders spring from simple rules repeated without end.”
I think that much of our lives works this way.
And part of what I am interested to do with this blog is to find, and apply, some of those simpler rules.