Fractal Image “White Swords”

Some people though that mathematics is fun, challenging, or brain-tearing, but how about beautiful?

Some of you may have already know about fractals – a geometry so elaborate that in any scale of magnification, the shape is still basically the same. A non-ideal example is trees: zooming in (looking at the branches) gives you a “mini-tree” shape; do that again and you get more mini-mini-trees, and so on. Real fractal trees look like trees even when you zoom in infinitely many times.

“Fractal Image Angels’ Rapiers”

The interesting part is that some natural objects have this very property (the trees mentioned, if you haven’t noticed, is a natural object). Also, humans like to see natural objects (if you don’t believe me, take a walk to a park and contrast the view with that of your desk). So, do humans like fractals? It turns out that some fractal images are, indeed, very beautiful to our eyes! It turns out that a mix of mathematical functions, colors, and luck (hey, we randomize things, and getting a bad image is easier than getting a good one) can become a feast for the eyes.

Fractal Image “I See Dolphins”

Another, better news is that you can make fractal images with a program named Apophysis especially made for people that have no work to do besides viewing fractals. Apophysis does just that: mixing mathematical functions, colors, and luck for you. I myself have made a number of beauties using the program (aren’t the titles also beautiful?), some of them lingering in this post. A lot of sophisticated fractal images are also floating on the internet (here are some).

It is a wonder of nature that functions and numbers (and computers) can make such magnificent images. Just remember not to view them too long, okay?