and the Sierpinski triangle

The fractal that slowly appears on the main page is the Sierpinski triangle. It is there because I like to use its construction as a short story to try and convey the appeal of mathematics to those who do not understand, or enjoy it.

The story starts by explaining how one can draw the triangle by following a very simple few steps.

- First you mark the three corner points of the triangle. You select one of the points and mark it with a dot.
- Then, you randomly choose one of the three corner points and you draw a dot exactly halfway between the last drawn dot and the chosen point.
- This last step you repeat a few million times and like magic, the Sierpinski triangle will emerge.

There are other techniques to draw the triangle, but what I like about this one, is the feeling of magic that it can inspire in people. This, I feel, is the appeal of mathematics. It all starts with the consideration of a few simple rules or assumptions, and upon executing them, deducing their implications, the most intricate and marvellous structures may arise, unexpectedly.