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. 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 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 Browns ( 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.

‘The City Of God is a personal project to come out of my research for the flowers commission of the Four Seasons Dubai,’ he writes on his Flickr. ‘The idea was to investigate parallels between the super-complex geometries seen in Islamic architecture and super-detailed recursive fractal patterns.’

This hyper-complex set of patterns is mesmerizing. The link to Islamic architectural geometries is interesting: even more interesting is the fact that some of these shots actually look like a city, in the future – an architectural style that doesn’t exist right now, but might.

But the real caveat is Dantillon: the Brutal Deluxe.

This is, undoubtedly, a city. it’s a strange city – but it looks like something that might very well exist in a hellishly overcrowded future. It even looks strangely organic, as if it was grown and not entirely planned.

“Brown begins with a program by plugging random numbers into the program, which uses fractal mathematics to create unique shapes that resemble a 3-D graph,” writes Wired, which spoke about Brown in 2016. “He spends several hours “exploring” the terrain until he finds an interesting form. Brown isolates the shape, and tweaks it until he arrives at something he likes. Then the program applies bits and pieces of public domain photos of 1970s apartment buildings. The result is hulking, maze-like structures that appear to go on forever.”

If you look close enough you can even make out the windows in the apartments. William Gibson actually used it for the the new cover of Neuromancer, saying it was exactly like he’d imagined the Sprawl to be.

What does this mean?

Leave out the bizarre beauty of the whole premise. Leave out the artistic value for now.

Cities are constantly evolving entities. And right now, our cities are a bit inefficient. Yes, some are beautiful, but they generally do a bad job of providing space for every who wants to live there – hence the steep costs of living. There’s absolutely no question that our cities, by process of acquisitions, developments and designs, will head towards a Dantillon or City of God-esque future.

More Dantillon.

This is where fractals play in. Perhaps architects can use this kind of fractal-based architecture for ideas they never would have come up with on their own. Perhaps we might use them for futurism: if we know they match existing architectural patterns, I can imagine software using a blueprint of, say, London, to show how it might organically grow and look in the future. The fact that fractals are capable of mimicking human architecture – and not just road networks and clusters of buildings, but more detail like in Dantillon – makes this strange art absolutely unavoidable.

Or perhaps – as we rebuild over existing cities, even colonize new planets – we might build our cities the way Daniel Brown builds his: feed numbers to a program and watch the fractals grow.


To learn more about M-sets:

To explore Daniel Brown’s work: