Peano Curve is Fractal

Theorem

The Peano curve is a fractal with similarity dimension of $2$.

Hence it is an example of a fractal with a similarity dimension which is an integer.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Peano's curve
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Peano's curve