In  one of  the problem sets, I have  given  a problem on
Koch triangle.  I  took this opportunity to teach them about fractals
and fractal dimensions.


This gif animation shows scale invariance.  In every scale (as you zoon in or zoom out) you see
the same structure.  Remember, ploting y= x*x in the same window in [-1,1] and then in [-100,100].
ypu can not distinguish.

Here is a java applet of Koch curve. Just look around you will find some more applets here.

There are many web-sites, which  explains fractals.   I will add some links
here.