posted on (deprecated) site on February 21, 2017

It was Arthur C Clarke who introduced me to fractals.

To be specific, it was The Ghost from the Grand Banks, a novel he published in 1990.  In it, Edith Craig, a mathematician, spends her time plotting the Mandelbrot set on a computer screen. Eventually, drawn to the strange Neverlands it sketches on her screen, Edith becomes one of a strange band of reclusive explorers who spend their lives mapping out the far corners of the Mandelbrot set. They share little discoveries – ‘islands’ and ‘seas’ – real-life analogues drawn by a mathematical equation.

It was probably not Clarke’s best work. I barely remember the main plot. But the fractals stuck with me.  Something about it reminded me of a childhood favourite: Peter Pan, by J.M. Barrie, saying

“If you shut your eyes and are a lucky one, you may see at times a shapeless pool of lovely pale colours suspended in the darkness; then if you squeeze your eyes tighter, the pool begins to take shape, and the colours become so vivid that with another squeeze they must go on fire.”

When I managed to find a Java applet that drew the M-set out for me, I clicked and prodded in childish wonder at the nebula-like multicolored Neverland it built for me.


From Malin Christersson’s blog. From left to right, the fractal is being zoomed in – and you see the features developing as we do so. Some of these visuals even have names. Seahorse Valley. Elephant Valley.

I saw trees, islands, neurons- enough to keep me occupied for a long time. You see even stranger things when you go 3D.


The tribox, from Skytopia. Notice the Alien-esque visuals.

Ever since then, I’ve been not-so-systematically cataloging the uses of fractal visualizations. Out of everything I’ve seen, the most eye-catching use is …

City design.

Daniel Brown is an architect, designer and programmer. He’s pretty famous in certain circles – especially anything that has to do with generative architecture. Both Jonathan Ive (Apple) and William Gibson (Neuromancer) are fans of his work, and that’s high praise.

I first came across his work in 2013, when the Daily Mail (UK) ran an article about a paralyzed designer who created flowers out of mathematical formulae.

Like these.


Daniel used an algorithm to create a flower form that he then adapted to create new, individual ‘species’  all of them distinct, but so plausible-looking. Throw time forward a bit, and Daniel Brown pops up on my feed again; this time, with something far more complex: the City of God.