Fractals, Symmetry and Organisation

One of the most fascinating aspects of fractal images is the extent to which they display similar proportionality to natural objects. In the Mandelbrot set, for example, we can see the golden-section ratios (Phi) clearly.





Such symmetry exists temporally too, most notably in music. I was always fascinated by Lendvai's analysis of Bartok:

At the moment, I'm wrestling with the idea of proportion and symmetry in learning and educational organisations. Often as teachers we instinctively know when to 'change the pace' or 'do something different'. Bartok's 'instinct' (and Debussy's too as Roy Howatt informs us) has a number, and it's the golden ratio.

Fractals are pretty simple, and may be useful as 'symmetry generators' in some sort of simulation of organisations and learning. The question is, how might this be done, and what might it mean?