Lorenz in the Browser, or Why Tiny Rounding Errors Become Weather Drama
The Lorenz sketch feels almost polite until you watch it long enough. Six nearby points start together, then peel away and loop into different arcs, while all of them stay trapped inside the same butterfly shape. That tension is why this model still lands so hard. It is deterministic, yet long-range prediction breaks because tiny differences blow up fast. Lorenz showed this in his 1963 paper on deterministic nonperiodic flow while modeling atmospheric convection, and the famous butterfly framing came later in his 1972 predictability talk. The metaphor got popular because it is vivid, though the deeper point is practical. Even with fixed equations, uncertainty in initial conditions sets a horizon on what forecast skill can do.
p.x += sigma * (p.y - p.x) * dt;
p.y += (p.x * (rho - p.z) - p.y) * dt;
p.z += (p.x * p.y - beta * p.z) * dt;
In this browser version, the constants are the classic set, sigma 10, rho 28, and beta 8/3, and that is enough to produce the iconic attractor with no extra ornament. I like this piece because it teaches with motion instead of lecture notes. You drag to rotate, reseed, and immediately see that two starts that look identical on screen can diverge into separate trajectories after a short while. If you want to run it directly, open the artifact and then wander through the rest of the collection from the gallery index.
Links. Visualization · Gallery Index · Lorenz system background · Butterfly effect background
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