The Lorenz Attractor is a classic example in Chaos Theory, developed by Edward Lorenz, the founder of the field. This model visually represents a set of differential equations originally formulated to model atmospheric convection. The Lorenz Attractor is significant because it illustrates how chaotic systems can behave, where even the slightest change in initial conditions can lead to drastically different outcomes. The lines on the attractor never overlap, and if the attractor is initialized at two points, the pathways diverge and bear no resemblance.
The three differential equations are:
x' = σ(y - x)
y' = x(ρ - z) - y
z' = xy - ßz