## fractals

The idea that simple mathematical rules govern complex behaviour in nature is the basis of chaos theory and fractals.

There is a nice applet on the cut-the-knot website that generates a Sierpinski triangle from a random process. This is fun to do with students by hand, although it does take quite a while to get a good pattern! This is connected to the Pascal's cube task!

Changing the number of vertices and distance plotted from the vertex creates other patterns such as these, where n is the number of vertices and r is the distance plotted from the current point to the new vertex (below). I haven't found a way to make this into a lesson yet, maybe you have a suggestion?

Changing the number of vertices and distance plotted from the vertex creates other patterns such as these, where n is the number of vertices and r is the distance plotted from the current point to the new vertex (below). I haven't found a way to make this into a lesson yet, maybe you have a suggestion?

The Koch snowflake is also fun to create and leads to an interesting discussion about perimeter and area. I have used this with year 7 students to some success, drawing the shapes on triangle dotty paper to help find the area/perimeter. I feel this could be developed for work with geometric series (C2).

This leads nicely onto the section on chaos theory.

This leads nicely onto the section on chaos theory.