PeanoCurve

PeanoCurve[n]

gives the line segments representing the n^(th)-step Peano curve.

Details and Options

  • PeanoCurve is also known as Peano space-filling curve.
  • PeanoCurve returns a Line primitive corresponding to a path that starts at {0,0}, then joins all integer points in the 3n-1 by 3n-1 square, and ends at {3n-1,3n-1}. »
  • PeanoCurve takes a DataRange option that can be used to specify the range the coordinates should be assumed to occupy.

Examples

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Basic Examples  (2)

A 2D Peano curve:

Lengths of the approximations to the Peano curve:

The formula:

Visualize the Peano curve in 2D with splines:

Scope  (6)

Curve Specification  (2)

A 2D Peano curve:

The n^(th) approximation of the Peano curve:

Curve Styling  (4)

Peano curves with different thicknesses:

Thickness in scaled size:

Thickness in printer's points:

Dashed curves:

Colored curves:

Options  (1)

DataRange  (1)

DataRange allows you to specify the range of mesh coordinates to generate:

Specify a different range:

Applications  (4)

PeanoCurve is constructed recursively by transforming segments into curves linked together by lines:

Next iteration:

Visualize the Peano curve in 2D:

With splines:

Build a simple polygon:

Apply a Peano curve texture to a surface:

Properties & Relations  (3)

PeanoCurve consists of lines:

Find the perimeter of the 2D Peano curve:

DataRange->range is equivalent to using RescalingTransform[{...},range]:

Use RescalingTransform:

Possible Issues  (2)

By default, the coordinates of a Peano curve are not in the unit square:

Using DataRange to generate a Peano curve in the unit square:

PeanoCurve can be too large to generate:

Neat Examples  (1)

Traversal animations:

Introduced in 2017
 (11.1)