Tilings of 5-Fold Rotational Symmetry: II.Tilings of 5-Fold Rotational Symmetry: III.Tilings of 5-Fold Rotational Symmetry: IV.Tilings of 5-Fold Rotational Symmetry: V.Tilings of 5-Fold Rotational Symmetry: VI.You can play with these images using my browser app at This is similar to the Sierpinsky triangle, which is covered by triangles of different sizes if one looks at the complementing space, and to the Apollonian Gasket, covering a circle with small circles. Actually, the entire surface of the fractal hexagon is covered by these snowflakes. A diverse set of businesses and industries across the world, we work together to keep improving and exploring new ways to make life even better. Inside you see white Koch snowflakes of different sizes. Based in Wichita, Kansas, Koch Industries is one of the largest private companies in America. The grey area surrounding the hexagon is the outside of an “inverted” Koch snowflake. But it is more interesting to look at the space in between and outside. The black pixels approximate the fractal hexagon. This is the result after repeating this procedure seven times: Fractal hexagon: An fractal storm of Koch’s snowflakes The Feigenbaum attractor (see between arrows) is the set of points generated by successive iterations of the logistic function for the critical parameter value λ ∞ = 3.Sierpinsky’s hexagon: Replace a hexagon by six smaller ones. Presented here is a list of fractals, ordered by increasing Hausdorff dimension, to illustrate what it means for a fractal to have a low or a high dimension.ĭeterministic fractals Hausdorff dimension According to Benoit Mandelbrot, 'A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.'

Hexagon koch