Basic Examples (2) 

The points forming a 1^st-step Koch curve:

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A 1^st-step Koch curve visualization:

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Visualizations of the 2^nd through 5^th-step Koch curves:

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A 2^nd-step Koch curve in 3 dimensions:

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Scope (5) 

Form Koch curves over a 2D list of points:

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Form Koch curves over a 3D list of points:

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Change the path direction of the 2D Koch curve:

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Change the path angle of the 3D Koch curve:

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A representation of how the angle rotates the 3D Koch curve, where the 0 angle is in black:

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The 0^th-step Koch Curve does not introduce any new points:

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Options (2) 

Setting "ExactValues" to False causes the output to be imprecise:

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Imprecise outputs are much faster to compute:

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Applications (2) 

Form a Koch snowflake by specifying the corner points:

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Invert the Koch snowflake:

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A matrix of the first six steps of Koch snowflakes from the first six regular polygons:

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Properties and Relations (1) 

The Koch snowflake can be generated with either KochCurve or KochCurvePoints:

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Possible Issues (1) 

If a point or the value of the orientation is inexact, then parts of the output will return inexact:

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Neat Examples (4) 

Increasing the density of lines gives the impression of a solid object:

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Visualize the increasing detail of higher-step Koch curves:

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Apply the Koch Curve to other named curves:

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An overlap of the Koch Snowflakes generated from the first 10 regular polygons:

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The same Koch Snowflakes when the orientation is reversed:

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