Fractal is a term invented by Benoit Mandelbrot to describe complex patterns which also have an element of repitition. An example is a cauliflower or brocolli, where a stem taken from the main vegatable will itself look like a miniature main vegetable.
 
A simple way to see how fractals work is to look at how one, the Sierpinski Gasket, is formed.

The key lesson is that underneath complexity SIMPLE RULES ARE OPERATING. The critical issues for leaders facing complexity is to identify and understand the underlying simple rules. These will differ depending on context. But they will be there.
There are some more lessons to learn from the Sierpinski Gasket  look at the brief film below.......

So a seemingly chaotic random approach can get the same result as a deterministic managed approach. Sometimes the deterministic approach is better (as in this case) and sometimes the random chaotic approach is better (see film). It takes an appreciation of complexity science and chaos theory to know when which approach is better. It also takes a wider view of what leadership is.
And because something looks chaotic, it does not necessarily mean it is. The final lesson from the Sierpinski Gasket is that you can start at completely different starting points, but if you use similar rules you can get broadly similar results as the graphic below shows.

So the key three lessons from fractals which are important for leadership are:

