The lorenz system (lorenz attractor) is a system of ordinary differential equations. It was first studied by Edward Lorenz.
It is based on following ordinary differential equations:
Since we want to define the time-step-size per draw loop, we define dt and multiply each equation by dt. This gives us:
Now, we define the values of the constants rho, sigmoid and beta. This gives us:
We can use these three formulas to calculate the changes of x, y and z of of points. Therefore we have to add the changes to the current values, which gives us a new point (x + dx, y + dy, z + dz) -> t + td -> (x, y, z).