# SierpinskiCurve

gives the line segments representing the n -step Sierpiński curve.

# Details and Options • SierpinskiCurve is also known as Sierpiński space-filling curve.
• SierpinskiCurve returns a Line primitive corresponding to a closed path around {0,0}.
• • SierpinskiCurve 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 Sierpiński curve:

Lengths of the approximations to the Sierpiński curve:

The formula:

Visualize the Sierpiński curve in 2D with splines:

## Scope(6)

### Curve Specification(2)

A 2D Sierpiński curve:

The  approximation of the Sierpiński curve:

### Curve Styling(4)

Sierpiński 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)

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

Next iteration:

Visualize the Sierpiński curve in 2D:

With splines:

Build a polygon:

Apply a Sierpiński curve texture to a surface:

## Properties & Relations(3)

SierpinskiCurve consists of lines:

Find the perimeter of the 2D Sierpiński curve:

DataRangerange is equivalent to using RescalingTransform[{},range]:

## Possible Issues(2)

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

Using DataRange to generate the Sierpiński curve in the unit square:

SierpinskiCurve can be too large to generate:  ## Neat Examples(1)

Traversal animations:

Introduced in 2017
(11.1)