# Definition:Peano Curve

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## Definition

A **Peano curve** is a fractal curve which can be written as a Lindenmayer system.

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## Source of Name

This entry was named for Giuseppe Peano.

## Historical Note

The original Peano curve was invented by Giuseppe Peano as a demonstration of a continuous curve that completely fills a square.

Many such curves have been invented since then, many of which are considerably simpler than the one invented by Peano.

## Sources

- 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.33$: Weierstrass ($\text {1815}$ – $\text {1897}$) - 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** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**Peano curve**