h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I became intrigued by fractal shapes when I found a diagram in one of Mandelbrot's books of a L-System Fractal (see posting on Fractint to generate examples)that looked like a tree. By varying one of the parameters, he showed how it could look from anything from a low bush, to a tree, to cracks in a dried riverbed. However, one of the shapes reminded me of something I saw in my working life: the road layout of a typical modern British housing estate.

I looked into this oddity and found that I could generate an identical looking fractal from a simple rule: fit as many housing plots as possible onto a 2-dimensional plane connnecting them with the shortest length of road.

It seemed to me that there was a fundamental truth here. Fractals need not only be an inevitable crystallisation of a natural process (ferns, trees, lightening etc) but could be inadvertently man-made.

Christopher Alexander (the subject of a future entry I think) wrote a book called "A New Theory For Urban Design" which seems to use the idea of fractals (and its cousin Chaos Theory) to create better towns and man-made places; written well before the terminology became common. Perhaps one day we will know enough about this odd geometry to use it to create better looking places that have the organic qualities we admire so much in old towns and cities. Alternatively, they may end up looking like broccoli.

"I've only lived in Asparagusville. What's it like in Pus Town?"

I think that the housing estate solution shows that nature takes the most efficient route to organisation, same as us. This could be an interesting topic for research - the effiency of fractal structures as a solution to various natural structural development problems.

I believe it true that nature uses irrational number sequences in plant structures?

I suspect nature 'knows' more about the complexity of numbers than we do.