Have you heard of this thing called the "Butterfly Effect"? Essentially, it states that the smallest changes in a system result in large changes at a later point in time. The existence of this effect largely came into our understanding when we first started predicting weather. This is why it's called the "Butterfly Effect". The belief is that even a miniscule disturbance of the air due to a butterfly flapping its wings results in storms/hurricanes halfway across the world.
The Lorenz attractor is a set of chaotic solutions of the Lorenz system. The Lorenz system is a system of ordinary differential equations first studied by Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.
Generally, only quantum systems and effects are known to have unpredictable effects. The Lorenz Attractor systems shows that physical systems can be completely deterministic and yet still be inherently unpredictable. I think it is poetic that the shape of the Lorenz attractor itself resembles a butterfly.
The forumlae for this animation below are taken from the
wiki site for the Lorenz System.
The whole system works on the following 3 differential equations. These are known as the Lorenz equations.
dx / dt = a(y - x)
dy / dt = x(b - z) - y
and
dz / dt = xy - cz
Keep in mind that the equations describe the rate of change of 3 weather related quantities with respect to time (dt).
x is proportional to the rate of convection,
y to the horizontal temperature variation,
and z to the vertical temperature variation.
The constants a, b, and c are system parameters proportional to the Prandtl number, Rayleigh number,
and certain physical dimensions of the layer itself.
| Presets | ||
| 1 | a = 10, b = 28, c = 8/3 | |
| 2 | a = 10, b = 13, c = 8/3 | |
| 3 | a = 10, b = 14, c = 8/3 | |
| 4 | a = 10, b = 15, c = 8/3 | |
| 5 | a = 10, b = 50, c = 4 | |
| 6 | a = 10, b = 45, c = 10 | |
| 7 | a = 10, b = 65, c = 12 | |
| 8 | a = 10, b = 28, c = 10 | |