Interactive Lab / The Cantor Set

Iterated Function System Discovered 1874 / 1883 Dimension log 2 / log 3 ≈ 0.631

The Cantor Set

C0=[0,1],Cn+1=Cn3∪(Cn3+23)C_0 = [0,1], \qquad C_{n+1} = \frac{C_n}{3} \cup \left(\frac{C_n}{3} + \frac{2}{3}\right)
★Cool Fact
The Cantor set has zero total length, yet it's uncountable — the same cardinality as the interval it's cut from. A set can be simultaneously “almost nothing” by one measure and “just as big as everything” by another.

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