Koch Snowflake - Variants of The Koch Curve

Variants of The Koch Curve

Following von Koch's concept, several variants of the Koch curve were designed, considering right angles (quadratic), other angles (Césaro) or circles and their extensions to higher dimensions (Sphereflake):

Variant Illustration Construction
1D, 85° angle The Cesaro fractal is a variant of the Koch curve with an angle between 60° and 90° (here 85°).
1D, 90° angle
1D, 90° angle
1D, ln 3/ln (√5)
1D, ln 3.33/ln (√5) Another variation. Its fractal dimension equals ln 3.33/ln (√5)=1.49.
2D, triangles
2D, 90° angle Extension of the quadratic type 1 curve. The illustration at left shows the fractal after the second iteration .
2D, 90° angle Extension of the quadratic type 2 curve. The illustration at left shows the fractal after the first iteration.
3D, spheres Eric Haines has developed the sphereflake fractal, which is a three-dimensional version of the Koch snowflake, using spheres.

Read more about this topic:  Koch Snowflake

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