Famous Fractals   

Lorenz Attractor

Lorenz Attractor is one of the most famous strange attractors. It was discovered by Lorenz, who was studying the patterns of weather change. Lorenz came up with three formulas that could approximately model the weather. These formulas are the following:

dx/dt = –ax + ay
dy/dt = bx – y –xz
dz/dt = –cz + xy
(The formulas use derivatives, which is a topic studied in calculus)

The most commonly used values for a, b, and c are 5, 15, and 1 respectively. If the formulas with these three values are used to generate a 3-dimensional strange attractor, the figure formed is the following:

Although it might not seem so right away, this figure is a fractal since magnifying it does not decrease the amount of detail: