Peano Curve

Peano curve

[pā′än·ō ‚kərv]

(mathematics)

A continuous curve that passes through each point of the unit square.

Peano Curve

a continuous curve in the Jordan sense that entirely fills a square—that is, the curve passes through all the points of the square. The first example of a curve possessing this

Figure 1

property was constructed by G. Peano in 1890, and a simple example of a Peano curve was given by D. Hilbert in 1891. The initial steps of Hilbert’s construction are illustrated in Figure 1.

The limiting curve obtained by continuing the construction ad infinitum will be a Peano curve that passes through all the points of the square D.

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References in periodicals archive ?

We found that Peano curve is self-similar, Moore curve is not self-similar, Meander curve is self similar and Lebesgue curve is self-similar.

Having in view the geometrical characteristics, the Peano curve fractal may be used for heat pipe device.

For example a Peano curve is built by Hilbert (Fig.

A new heat pipe cooling device

In this example, we will look on the Peano curve and show how we can construct a Chinese lattice based on this curve.

Let us recall the shape and properties of the Peano curve.

In order to create a Peano curve we will need an L-system with the following axioms:

Let us start with a simple command to create the Peano curve of second generation in MuPAD.

An algorithmic approach to Chinese lattice design

This coding technique could be successfully applied to the generation of other regular space-filling curves, such as the Peano curve.

This would enable the construction of other forms of space-filling curve, such as the Peano curve.

On the geometrization of the Peano curve and the arithmetization of the Hilbert curve.

Algorithm 781: Generating Hilbert's Space-Filling Curve by Recursion

All well-known fractal curves, such as Koch curve [13], Peano curve [22], Giuseppe Peano curve [17], and Hilbert Curve [23, 24], are preferably designed into dipole or monopole antennas.