# KochCurve

KochCurve[n]

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

KochCurve[n,{θ1,θ2,}]

takes a series of steps of unit length at successive relative angles θi.

KochCurve[n,{{r1,θ1},{r2,θ2},}]

takes successive steps of lengths proportional to ri.

# Details and Options

• KochCurve is also known as Koch snowflake.
• KochCurve[n] is generated from the unit interval by repeatedly removing the middle third of the subsequent cells and replacing it with a triangle. »
• KochCurve[n] is equivalent to KochCurve[n,{0,60 °,-120 °,60 °}].
• KochCurve 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 Koch curve:

Lengths of the approximations to the Koch mesh:

The formula:

The first four iterations of the Koch snowflake:

## Scope(7)

### Curve Specification(3)

A 2D Koch curve:

The n approximation of the Koch curve:

Specify the length of the relative angles:

### Curve Styling(4)

Koch 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)

KochCurve is generated by repeatedly removing the middle third of the cells and replacing it with a triangle:

Generate Cesàro fractal:

## Properties & Relations(3)

KochCurve consists of lines:

AnglePath can be used to generate the first iteration of the Koch curve:

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

## Neat Examples(1)

Koch snowflake in animation:

Wolfram Research (2017), KochCurve, Wolfram Language function, https://reference.wolfram.com/language/ref/KochCurve.html.

#### Text

Wolfram Research (2017), KochCurve, Wolfram Language function, https://reference.wolfram.com/language/ref/KochCurve.html.

#### CMS

Wolfram Language. 2017. "KochCurve." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/KochCurve.html.

#### APA

Wolfram Language. (2017). KochCurve. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/KochCurve.html

#### BibTeX

@misc{reference.wolfram_2024_kochcurve, author="Wolfram Research", title="{KochCurve}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/KochCurve.html}", note=[Accessed: 20-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_kochcurve, organization={Wolfram Research}, title={KochCurve}, year={2017}, url={https://reference.wolfram.com/language/ref/KochCurve.html}, note=[Accessed: 20-July-2024 ]}