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Peano Curve

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The Peano curve is one of a number of fractal curves associated with Peano.

PeanoCurve

It is the fractal curve illustrated above which can be written as a Lindenmayer system.

PeanoCurve2

The nth iteration of the Peano curve illustrated above curve is implemented in the Wolfram Language as PeanoCurve[n].

See also

Dragon Curve, Hilbert Curve, Lindenmayer System, Sierpiński Curve

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References

Dickau, R. M. "Two-Dimensional L-Systems." https://www.robertdickau.com/lsys2d.html.Hilbert, D. "Über die stetige Abbildung einer Linie auf ein Flachenstück." Math. Ann. 38, 459-460, 1891.Mandelbrot, B. B. The Fractal Geometry of Nature. New York: W. H. Freeman, pp. 62-63, 1983.Peano, G. "Sur une courbe, qui remplit une aire plane." Math. Ann. 36, 157-160, 1890.Pegg, E. Jr. Mathematical Games. Episode 16: "Space-Filling Curves." Apr. 18, 2024. https://www.youtube.com/watch?v=3qbZadltTCI.Wagon, S. Mathematica in Action. New York: W. H. Freeman, p. 207, 1991.

Referenced on Wolfram|Alpha

Peano Curve

Cite this as:

Weisstein, Eric W. "Peano Curve." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PeanoCurve.html

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