Tiny WorldsMore experiments by @juyeam ↗
AN EXPERIMENT IN SENSITIVITY

One millionth.
Two different paths.

Change only the starting x. Keep every rule the same.

A · start x = 1B · start x = 1.000001
Two computed Lorenz paths, projected onto x and z01020304050zx-20-1001020

Faint lines: full paths. Bright lines: the last 2 simulated time units.

Deterministic does not mean easy to predict.

Astra built this numerical experiment. No AI call runs when you change a control. With a starting difference of 0.000001, the separation at t = 30 is about 13.619.

What the picture can tell you

Lorenz equations, σ = 10, ρ = 28, β = 8/3. RK4 time step 0.000125; display samples every 0.01. The picture uses x and z; separation uses all three coordinates. Roundoff and integration error also grow. These are numerical paths, not exact long-term forecasts.

Download the Python check ↗Source: Lorenz (1963) ↗