Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, and art.

Fractal patterns have been modeled extensively, albeit within a range of scales rather than infinitely, owing to the practical limits of physical time and space.

Fractal patterns have been reconstructed in physical 3-dimensional space and virtually, often called " in silico " modeling.

Fractal patterns also use magnification or scaling giving an effect known as self-similarity or scale invariance.

Like a Fractal, the top can be a bottom, and a bottom can be a top, and the patterns evident at one level can be similar to those at another.

It was assumed that Fractal art could not have developed without computers because of the calculative capabilities they provide.

Martelli and Canning realized that the crystal structures that have identical interstitial regions are actually not the most ideal structure for practical applications and pointed out aperiodic structured fibers, such as Fractal fibers, are a better option for low bend losses.

Aside from traveling through dimensions, having Fractal Knots, and being attracted to electromagnetic hot-spots, they have very little in common with each other.

Records have also had music released and reissued by labels such as La Musica, Charnel, Riot Season, Squealer, Fractal, aRCHIVE, Assommer and etc.

" Following Benoit Mandelbrot's 1999 Scientific American article " A Fractal Walk Down Wall Street ," the Theorist ran detailed criticism of that article, saying that Mandelbrot took credit for ideas that " originated with Ralph Nelson Elliott, who put them forth more comprehensively and more accurately with respect to real-world markets in his 1938 book The Wave Principle.

Fractal Glider is the stage name of Paul McCosh, a psychedelic trance artist from Melbourne, Australia.

Techniques in Fractal Geometry.

* Benoît B. Mandelbrot The Fractal Geometry of Nature.

The Science of Fractal Images.

* Huajie Liu, Fractal Art, Changsha: Hunan Science and Technology Press, 1997, ISBN 9787535722348.

Physics and Fractal Structures ( Foreword by B. Mandelbrot ); Masson, 1996.

The basic patents covering Fractal Image Compression, U. S. Patents 4, 941, 193, 5, 065, 447, 5, 384, 867, 5, 416, 856, and 5, 430, 812 appear to be expired.

* Fractal compression.

Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media.

Fractal art developed from the mid 1980s onwards.

Fractal art ( especially in the western world ) is not drawn or painted by hand.

As stated by Kerry Mitchell in The Fractal Art Manifesto, " Fractal Art is a subclass of two-dimensional visual art, and is in many respects similar to photography — another art form that was greeted by skepticism upon its arrival.

Fractal images typically are manifested as prints, bringing fractal artists into the company of painters, photographers, and printmakers.

This is a format that traditional visual artists are quickly embracing, bringing them into Fractal Art's digital realm.

However, Fractal Art is clearly distinguished from other digital activities by what it is, and by what it is not.

Most importantly, " fractal art is simply that which is created by Fractal Artists: ART.

We are forced, in our behavior towards others, to adopt empirically successful patterns in toto because we have such a minimal understanding of their essential elements.

The markets for electronic parts in 1960 have reflected the changing patterns of the various end equipment segments of the industry.

Those species that breed in smaller water bodies or other specialised habitats tend to have more complex patterns of behaviour in the care of their young.

Any decline in amphibian numbers will have an impact on the patterns of predation.

Tooth wear patterns hint that complex head shaking behaviours may have been involved in tyrannosaur feeding.

Dendritic agates have fern like patterns in them formed due to the presence of manganese and iron oxides.

Limited possibilities have been explored by artists as an outlet to artistic expression, and has been cultivated to become a positive style and tradition, emphasizing the decorative function of art, or its religious functions via non-representational forms such as Geometric patterns, floral patterns, and arabesques.

to induce specific growth patterns in that one can easily prepare a solution containing the desired amount of hormone, add it to the known volume of GM, and autoclave to both sterilize and evaporate off any solvent that may have been used to dissolve the often-polar hormones.

"' Po Boy ', scored for guitar with lounge chord jazz patterns, ' almost sounds as if it could have been recorded around 1920 ," says Riley.

Humans have fundamentally altered global patterns of biodiversity and ecosystem processes.

Others, such as Claude Lévi-Strauss ( who was influenced both by American cultural anthropology and by French Durkheimian sociology ), have argued that apparently similar patterns of development reflect fundamental similarities in the structure of human thought ( see structuralism ).

This particular ecological niche buffered them from extinction .< ref > Similar, but more complex patterns have been found in the oceans.

Studies of the neuroscience of free will have also shown that the experiences that people report when they behave purposefully sometimes do not correspond to their actual behaviors or to the patterns of electrical activity recorded from their brains.

Certain stereotypical patterns of breathing have been identified including Cheyne-Stokes a form of breathing in which the patient's breathing pattern is described as alternating episodes of hyperventilation and apnea.

In stream communities few animal groups became extinct because stream communities rely less directly on food from living plants and more on detritus that washes in from land, buffering them from extinction .< ref > Similar, but more complex patterns have been found in the oceans.

Different patterns of wood bracing have been used through the years by luthiers ( Torres, Hauser, Ramírez, Fleta, and C. F.

Several patterns of linking the rings together have been known since ancient times, with the most common being the 4-to-1 pattern ( where each ring is linked with four others ).

For these non-traditional applications, hundreds of weaves or patterns have been invented.

Traditionalist Roman Catholic groups, congregations and clergymen, however, continue to support missionizing Jews according to traditional patterns, sometimes with success ( e. g., the Society of St. Pius X which has notable Jewish converts among its faithful, many of whom have become traditionalist priests ).

Nevertheless, caches have proven themselves in many areas of computing because access patterns in typical computer applications have locality of reference.

Additionally, websites such as Etsy and Ravelry have made it easier for individual hobbyists to sell and distribute their patterns or projects across the internet.

Crochet patterns have an underlying mathematical structure — the pattern created by the regular presence or omission of stitches is the very essence of this artform.

It has been especially influential in software engineering where patterns have been used to document collective knowledge in the field.