The Mandelbrot Set

Take a point c on the complex plane, start at z = 0, and repeat z → z² + c over and over. If z stays bounded forever, c belongs to the Mandelbrot set (drawn in black). If it escapes toward infinity, the point is colored by how quickly it got away. That's the whole rule, yet the boundary of the set is endlessly intricate: zoom in anywhere along the edge and you'll find spirals, seahorse tails, lightning branches and tiny copies of the whole set, with no bottom to reach.

Benoit Mandelbrot made the set famous in 1980 while studying fractals at IBM, using some of the first computer graphics able to show it. It's a fitting cousin to markets: Mandelbrot later argued that price charts are fractal too, looking statistically alike whether you view a day or a decade. See Wikipedia for more.

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Rendering… · Click to zoom in 4×, right-click or shift-click to zoom out. More iterations reveal finer detail when you're deep in, but take longer to draw.

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Markets are fractal too: guess the timescale

Mandelbrot's favorite demonstration: strip the dates and axes off a price chart and nobody can tell a single afternoon from a decade. Below are four real SPY price paths from our database: one trading day of minute bars, one month of hourly bars, one year of daily closes, and ten years of monthly closes. Each is scaled to fill its box. Can you match them?