Smale's Horseshoe Map

The canonical example of deterministic chaos — stretch, fold, and the emergence of a Cantor set of infinite orbits

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Iteration: 0
How it works: The unit square is stretched vertically (×2.5), compressed horizontally (×0.4), then folded back over itself like a horseshoe.

Invariant set: Points that stay bounded under all iterations form a Cantor set — uncountably infinite, measure zero.

Symbolic dynamics: Each orbit is encoded as a bi-infinite sequence of 0s and 1s (which strip the point occupies).
Click "Symbolic Orbits" to track a point