Banes is taking a short break for the Thursday post, so I'll be filling in for a some unspecified number of posts. How many exactly? Well, how long is a piece of string? How long is the coastline of Britain? That was an academic paper ('How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension') by Benoit Mandelbrot, the guy who gave us fractals. If you're old enough to remember the 70s and early 80s, fractal patterns were everywhere. On T-shirts, posters, album covers, etc.



The interesting thing about fractals is that they don't conform to the standard common sense, or round number, of dimensions. A cube is dimension 3, a square 2, a line 1, and a point 0. But fractals can be, say, dimension 0.631, as in the Cantor Set. Named after Georg Cantor, the Cantor Set is created by taking the middle third from a line segment. This leaves two smaller line segments and a gap. Then you take the middle third from those two remaining line segments, meaning there are now four line segments and three gaps. Take the middle third from those four line segments, which creates eight smaller lines, and repeat to infinity …



If you've removed an infinite number of line segments how can there be anything left? Yet, you have also created an infinite number of (admittedly tiny) line segments. Does that mean it has infinite length? Mandelbrot showed the dimension was higher than a point (0), but lower than a line (1), coming in at about 0.631.

Fractals were really popular for a while. People tried to use them to analyze stock market movements, but while you can show the path the markets take is indeed a fractal, the mathematics offered no predictive power, so the financial world lost interest very quickly.

Nowadays if you see a fractal pattern it's probably in a movie or video game. Cloud formations, coastlines, snowflakes, nebula in space, mountain ranges, and other irregular phenomena can be generated in an eye-pleasing manner using fractal equations. Fractals have also found use in computer image compression, and I'm sure AI generators are using the mathematics of fractals to make videos of growing broccoli or evolving cloudscapes.

I was told to make a brief intro post, but this ramble on fractals probably tells you most of what you need to know about me. I'm the maker of musical themes for the Quackcast. I'm not making many comics at the moment, but I am writing a lot. I play bass, ukulele, and sometimes a theremin, as well as dabbling in other instruments. I used to write History of Science stuff, hence the details about fractals. And for a short while (maybe even just this once) I'll be writing the Thursday post on The Duck.

And if you're still wondering, the length of the coastline of Britain depends on what scale you measure it at. The more detailed the map, the longer the distance you can get for the same piece of coast. It's why Spain and Portugal used to give different results for the length of their shared border (987km, and 1,214km, respectively), and why the US Coastguard noted in 2006 that there was not, and could never be, an agreed upon definitive distance for its coastline.



— Gunwallace

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