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)
“I have been photographing our toilet, that glossy enameled receptacle of extraordinary beauty.... Here was every sensuous curve of the “human figure divine” but minus the imperfections. Never did the Greeks reach a more significant consummation to their culture, and it somehow reminded me, in the glory of its chaste convulsions and in its swelling, sweeping, forward movement of finely progressing contours, of the Victory of Samothrace.”
—Edward Weston (1886–1958)