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The Lorenz Attractor

$dxdt=σ(y−x)$ dtdx​=σ(y−x)

dydt=x(1−z)−y dtdy​=x(1−z)−y

dzdt=xy−bz dtdz​=xy−bz

This set of equations, known as the Lorenz attractor, is a classic example of a chaotic system. The Lorenz attractor is a set of chaotic solutions to the Navier-Stokes equations that describe the motion of fluids. The Mandelbrot Set

zn+1=zn!+c zn+1​=zn!​+c