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    The Beautiful Math Behind Hollywood's First Computer-Generated Sequence

    Written by

    Alex Pasternack

    Founding Editor

    You might think about big Hollywood movies these days not just as stories but increasingly as attempts to tackle tough problems. I don’t mean how to fix our educational system or our foreign policy. I mean how to make maximum returns off a multimillion dollar investment – and how to make magic look real. For the VFX whiz kids, this is actually a math problem. The movie is a kind of solution, and we decide if it’s right.

    The modern search for better solutions arguably began in the 1970s, with Hollywood’s special effects heavyweights turning to computers for the most cutting-edge film scenes – like the light bike races in Tron, which, as I wrote back when, gave rise to Perlin noise, which allowed the kind of computer-generated natural-looking surfaces that trick us into thinking that we’re really hunting the Opposing Force or visiting Pandora.

    That wouldn’t have been possible without a development a few years earlier. In the late 1970s, the graphics gurus at Industrial Light and Magic working on Star Trek II had to make a fly by sequence of the Genesis planet. Filming a model would not suffice. They would have to generate it entirely with the computer. But they couldn’t just pull off the wire-frame trick, the kind that had just been used in Star Wars for that Rebel briefing on the Death Star attack. This had to look natural. They would need to rely on fractals.

    By building the shapes of landscape features with fractals – from the Latin for fractured, the kind of mathematical shapes whose rough edges can mimic a great deal many of the irregularities found in nature – they would be able to generate a natural-looking landscape. This class of shapes generates lines that seem random, but which upon closer and closer inspection reveal inner patterns. Even when you can see a section of a fractal, the length you see would be infinite if you tried to measure the edges.

    Fractals were the discovery and the passion of Benoit Mandelbrot, the French mathematician whose reach spread far beyond his field. His just-released memoir, The Fractalist, writes the Times, isn’t a beautiful book, but it evokes the hard questions his work would answer: ‘What shape is a mountain, a coastline, a river or a dividing line between two river watersheds?’

    And those questions were the same ones that the CGI wizards at ILM faced as they began their work on Star Trek. And this is the solution they came up with, one that would change the landscape of computer generated film—or at least make it look a lot more real.

    This behind-the-scenes video explains the process:

    Fractals would also prove crucial in generating the geography of the moons of Endor and the Death Star outline in Return of the Jedi. The NOVA documentary “Hunting the Hidden Dimension” begins with a section of how fractals helped Hollywood:

    And if you want to do a bit of CGI on your own, the NOVA website includes a nifty “make your own fractal” application to get lost inside for hours.

    RIP Benoît Mandelbrot, Fractals Boss, Connoisseur of Chaos
    Arthur C. Clarke Explains Mandelbrot’s Fractals

    This post originally appeared on December 21, 2010.