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Beauty and Mathematics

This article entitled; Scientists teach a computer to recognize attractiveness in women reminded me of an overlay we used in software I wrote for plastic surgeons. The idea is we find faces more attractive if they follow a specific mathematical pattern. These images are more complex than the overlay I used but the idea is the same.

It’s called the golden ratio and there are a lot of examples on the web. Here is one where the author points out the basic idea. This is a video where a guy shows how you can use the images as overlays in Gimp or Photoshop.

The concept of beauty in mathematics has been around for a long time. In particular for physicists, it involves the ability to come up with an equation or small number of equations which describe the behavior of some complex physical system. A good example of this is Maxwell’s equations. In four simple equations Maxwell managed to describe both electricity and magnetism. Before he ‘unified’ these two forces, they were considered separate phenomena. Similarly, the holy grail of physics is to create a unified field theory which unifies the strong nuclear force, electromagnetism, the weak nuclear force, and gravity.

Wikipedia defines a fractal as;

“a rough or fragmented geometric shape that can be subdivided into parts, each of which is (at least approximately) a reduced-size copy of the whole,” a property called self-similarity.

There are endless fractal galleries on the web but I thought I would point out this site called chaoscope which has free fractal generating software. Also, if you are interested in the math, this site lists the formulas. For most cases if you click on the link it will show you an image for each formula.

Here is an image I created using a reflection of a Lyapunov fractal.

fractal image

Click here to see a larger view of the image.

Finally, it’s certainly not beautiful but I got a laugh out of this picture of high-rise trailers.

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