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
Famous quotes containing the words variants of, variants and/or curve:
“Nationalist pride, like other variants of pride, can be a substitute for self-respect.”
—Eric Hoffer (1902–1983)
“Nationalist pride, like other variants of pride, can be a substitute for self-respect.”
—Eric Hoffer (1902–1983)
“In philosophical inquiry, the human spirit, imitating the movement of the stars, must follow a curve which brings it back to its point of departure. To conclude is to close a circle.”
—Charles Baudelaire (1821–1867)
Related Phrases
Related Words