Search results
Results from the WOW.Com Content Network
According to Benoit Mandelbrot, "A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension." [ 1 ] 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.
Net. In geometry, the 120-cell is the convex regular 4-polytope (four-dimensional analogue of a Platonic solid) with Schläfli symbol {5,3,3}. It is also called a C 120, dodecaplex (short for "dodecahedral complex"), hyperdodecahedron, polydodecahedron, hecatonicosachoron, dodecacontachoron [1] and hecatonicosahedroid.
An n-flake, polyflake, or Sierpinski n-gon, [1]: 1 is a fractal constructed starting from an n-gon. This n-gon is replaced by a flake of smaller n-gons, such that the scaled polygons are placed at the vertices, and sometimes in the center. This process is repeated recursively to result in the fractal.
The regular dodecahedron is a polyhedron with twelve pentagonal faces, thirty edges, and twenty vertices. [1] It is one of the Platonic solids, a set of polyhedrons in which the faces are regular polygons that are congruent and the same number of faces meet at a vertex. [2] This set of polyhedrons is named after Plato.
The digits in the "odd place-intervals", i.e. between digits 2 2n+1 and 2 2n+2 − 1 are not restricted and may take any value. This fractal has upper box dimension 2/3 and lower box dimension 1/3, a fact which may be easily verified by calculating N(ε) for = and noting that their values behave differently for n even and odd.
Heighway dragon curve. A dragon curve is any member of a family of self-similar fractal curves, which can be approximated by recursive methods such as Lindenmayer systems.The dragon curve is probably most commonly thought of as the shape that is generated from repeatedly folding a strip of paper in half, although there are other curves that are called dragon curves that are generated differently.
The rhombicosidodecahedron shares the vertex arrangement with the small stellated truncated dodecahedron, and with the uniform compounds of six or twelve pentagrammic prisms. The Zometool kits for making geodesic domes and other polyhedra use slotted balls as connectors. The balls are "expanded" rhombicosidodecahedra, with the squares replaced ...
A dodecahedron and its dual icosahedron The intersection of both solids is the icosidodecahedron , and their convex hull is the rhombic triacontahedron . Seen from 2-fold, 3-fold and 5-fold symmetry axes