In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and y-directions. This means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation.

noun, plural com·mon·al·i·ties. a sharing of features or characteristics in common; possession or manifestation of common attributes.

In this page you can discover 12 synonyms, antonyms, idiomatic expressions, and related words for self-similar, like: birth-death, Ornstein-Uhlenbeck, , self-affine, topological, higher-dimensional, self-similarity, fractal, hyperbolic, low-dimensional and quasiperiodic. Trending topics.

It is well-known that the only regular polygons which tessellate the plane (using only one shape) are the triangle, square, and hexagon. The hexagon does not have this property, as one cannot form a larger regular hexagon from smaller regular hexagons. …

Part of the magic of snowflake crystals are that they are fractals, patterns formed from chaotic equations that contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical copy of the whole in a reduced size.

From a microscopic image analysis of the ice crystal particles, it was found that the perimeter of the ice crystal particles could be recognized as a fractal.

And then, of course, there are frozen fractals. A snowflake forms when a water droplet in the atmosphere freezes. The tiny bit of ice begins to fall to the Earth’s surface. As it falls, more water latches on to the forming snowflake and freezes. Ice crystals build upon ice crystals, forming a fractal pattern.

Fractal art is achieved through the mathematical calculations of fractal objects being visually displayed, with the use of self-similar transforms that are generated and manipulated with different assigned geometric properties to produce multiple variations of the shape in continually reducing patterns.

Fractal art (especially in the western world) is rarely drawn or painted by hand.

By now, the Axe-Fx has won every top award from every major guitar magazine. Four new artists become the “cornerstones” of our roster: Dweezil Zappa, Chris Traynor, Pete Thorn, and Larry Mitchell.

A fractal is a pattern that the laws of nature repeat at different scales. Examples are everywhere in the forest. Trees are natural fractals, patterns that repeat smaller and smaller copies of themselves to create the biodiversity of a forest.

Chaos is the study of how simple patterns can be generated from complicated underlying behavior. Chaos theory is really about finding the underlying patterns in apparently random data. It has been used to model biological systems, which are some of the most chaotic systems imaginable.

MIT, Harvard and UMass Medical School researchers have shown that DNA is actually organized as a fractal globule, right, which resists knotting and allows DNA regions on a chromosome to remain near each other in the 3D structure. Scientists have long known that DNA is arranged in a double helix.

It is the geometry of deterministic chaos and it can also describe geometry of mountains, clouds, and galaxies.” Al- though it is not widely known, the basic traits of a fractal can be applied to all aspects of life, because life exists in the form of a fractal abstraction.