Count On


The Fractal Factory

Welcome to The Fractal Factory. A random thing has no pattern right? Wrong!

To see why, we're going to carry out a simple random process many times, and each time leave a dot behind as a mark of where we've been. The dots make up an astonishing pattern.

We start with an equilateral triangle. Now comes the random process.

  1. First we decide on a starting point - move the cursor and click for your choice inside, outside or on the boundary of the triangle.
  2. Then we randomly select one of the vertices and then find the mid-point of the line joining it to the starting point. Click on the Start button to try it.
  3. Now the process is repeated, this time using the mid-point as a new starting point. We call the repeated application of such a process, iteration . Just click on the Start button to repeat the process again, and again ...

Did you see any pattern?