In 1963 Edward Lorenz was running a baby weather model on a Royal McBee LGP-30. He restarted a simulation halfway through, typing the state from a printout, and got a totally different forecast. The printout had three decimal places; the computer kept six.
$$ \dot x = \sigma(y - x),\quad \dot y = x(\rho - z) - y,\quad \dot z = xy - \beta z $$
That tiny initial-conditions discrepancy is what we now call sensitive dependence, or more cinematically, the butterfly effect. The shape on the page is the strange attractor — every trajectory ends up tracing it, but no two trajectories ever cross, and which lobe you're in next is, for practical purposes, unpredictable.
Drag ρ below ~24.74 and the chaos folds back into a stable spiral;
the attractor stops being strange. Push σ higher and the lobes get steeper.
Try β = 0.5 and watch the dynamics get strangled: less geometry, less room to breathe.
The deep point: this system has three variables, one differential equation each. There is nothing hidden, nothing random, nothing quantum. And it is, in practice, unforecastable.