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fract variations

Escape-time fractals are in a way the opposite of flame fractals. Both use the idea of an orbit: the sequence of points generated by repeatedly iterating fractal formulas. But while flame fractals plot the actual orbit points to create the flame, escape-time fractals use the orbit of a point to determine how to color it, commonly by determining how long it takes the orbit to cross an imaginary circle (or to “escape”; hence the name “escape-time”). The two methods usually generate very different fractals.

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Elliptic

The most commonly used coordinate systems are rectangular coordinates and polar coordinate. But these aren’t the only possibilities. One of the less common coordinate systems is elliptic coordinates. Although their mathematical application is specialized, they can be used in variations to make interesting flames.