In 1963, Edward Lorenz developed a simplified mathematical model for atmospheric convection. The model is a system of three ordinary differential equations now known as the Lorenz equations:

dx/dt = σ(x y)
dy/dt = ρ(r z) y
dz/dt = xy βz

Here x, y, and z make up the system state, t is time, and σ ρ β are the system parameters. The Lorenz equations also arise in simplified models for lasers, dynamos, thermosyphons, brushless DC motors, electric circuits, and chemical reactions.

From a technical standpoint, the Lorenz system is nonlinear, threedimensional and deterministic. The Lorenz equations have been the subject of at least one book length study (Wikipedia).

Lorenz system/equation is notable for having chaotic solutions for certain parameter values and initial conditions.

In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system.

Parameter used in this video:
Initial position = [0, 1, 1.05]
s = 10
r = 28
b = 2.667

Lorenz Attractor created using Python + Manim (plus some modification in Adobe Premiere Pro)
Source code: https://github.com/fajrulf/visualizat...