Modeled after a door key, the dental key was used by first inserting the instrument horizontally into the mouth, then its " claw " would be tightened over a tooth.

Modeled on the term “ racism ”, a large number of pejorative-ism terms have been created to describe various types of prejudice: sexism, ageism, ableism, speciesism, etc.

Modeled on the famous " Communist Manifesto " of the previous century, such manifestoes put forward ideas that were meant to provoke and to gather followers.

Modeled on the successful collaborative approach and the compression technologies developed by the Joint Photographic Experts Group and CCITT's Experts Group on Telephony ( creators of the JPEG image compression standard and the H. 261 standard for video conferencing respectively ), the Moving Picture Experts Group ( MPEG ) working group was established in January 1988.

Modeled after recent successes in downtown ballpark building ( such as San Francisco's AT & T Park ), and incorporating San Diego history in the form of the preservation of the facade of the historic Western Metals Company building ( now the left-field corner, the corner of the building substituting for the left field foul pole ), the new Petco Park is a sharp contrast to their previous home at Qualcomm ( Jack Murphy ) Stadium which was a cookie-cutter type football-baseball facility located in an outer, mostly commercial-industrial, area of the city near an interstate interchange.

Modeled after Homer's Iliad and Odyssey, the Aeneid follows the Trojan refugee Aeneas as he struggles to fulfill his destiny and arrive on the shores of Italy — in Roman mythology the founding act of Rome.

Modeled on that of China's, this ancient system has sustained a highly concentrated population and has made double-cropping wet-rice cultivation possible throughout about half the region.

" Modeled on their Red Dog experiences, on October 16, 1965, the Family Dog hosted " A Tribute to Dr.

His Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens ( Halle a / S: Verlag von Louis Nebert, 1879 ) ( Concept-Script: A Formal Language for Pure Thought Modeled on that of Arithmetic ) marked a turning point in the history of logic.

Modeled on Alexander Hamilton's First Bank of the United States the Second Bank began operations at its main branch in Philadelphia on January 7, 1817, managing twenty-five branch offices nationwide by 1832.

Modeled on Port Huron's first baseball club from 1867, the Welkin Base Ball Club re-creates the time of base ball's roots.

Modeled after the Old West towns seen in countless Hollywood films, Love Valley boasts a saloon, general store, hitching posts, and rodeos.

Modeled after New York City meatpacking district clubs, this restaurant and bar features high-end martinis, tapas, and jazz music.

Modeled after the Boar's Head Gaudy of Queen's College, Oxford, Boar's Head is the traditional start to the Christmas season at Oglethorpe.

Modeled after the Green Monster seats at Fenway Park in Boston, it seats up to 393 people and gives fans an opportunity to catch a home run ball.

Modeled after the North Atlantic Treaty Organization ( NATO ), CENTO committed the nations to mutual cooperation and protection, as well as non-intervention in each other's affairs.

Modeled after similar shelters in the Alps, the various huts hold from 36 people to 90 people.

Modeled on Spratt's Irish Constitutions, the regulations are comprehensive and well written, and are followed by an extended section devoted to songs.

Modeled on and loosely associated with Burning Man, Flipside is one of several Regional Burns around the USA.

Modeled after Bhutanese monasteries, or Dzong architecture.

Modeled after real-life " calendar girl " Tricia Stewart, Mirren has described Chris as a " dash in "— character who shared similarities with Stewart but was actually not based on her real persona.

Modeled on the Hollywood Walk of Fame, it honours the most illustrious people the Hong Kong film industry has produced over the past decades.

Modeled after the Washington Monument, the building was completed in 1929, months before the stock market crash in October of that year.

Modeled after the British special forces regiment, the Special Air Service, Delta Force is one of the best SOFs in the world.

A consequence of this structure is fractals may have emergent properties ( related to the next criterion in this list ).

Models may simulate theoretical fractals or natural phenomena with fractal features.

Also, these may include calculation or display artifacts which are not characteristics of true fractals.

Some, such as plant structures and coastlines, may be so arbitrary as to defy traditional mathematical description – in which case they may be analyzed by differential geometry, or as fractals.

Conway's Game of Life and fractals, as two examples, may also be considered mathematical puzzles even though the solver interacts with them only at the beginning by providing a set of initial conditions.

It also has a few " fractal types " that are not strictly speaking fractals, but may be more accurately described as display hacks.

Early examples of fractals which may be generated by an IFS include the Cantor set, first described in 1884 ; and de Rham curves, a type of self-similar curve described by Georges de Rham in 1957.

Some fractals may have multiple scaling factors at play at once ; such scaling is studied with multi-fractal analysis.

As mathematical equations, fractals are usually nowhere differentiable, which means that they cannot be measured in traditional ways.

The difference for fractals is that the pattern reproduced must be detailed.

In a concrete sense, this means fractals cannot be measured in traditional ways.

Also in the last part of that century, Felix Klein and Henri Poincaré introduced a category of fractal that has come to be called " self-inverse " fractals.

One often cited description that Mandelbrot published to describe geometric fractals is " a rough or fragmented geometric shape that can be split into parts, each of which is ( at least approximately ) a reduced-size copy of the whole "; this is generally helpful but limited.

According to Falconer, rather than being strictly defined, fractals should, in addition to being differentiable and able to have a fractal dimension, be generally characterized by a gestalt of the following features:

Images of fractals can be created by fractal generating programs.

L-systems can also be used to generate self-similar fractals such as iterated function systems.

Generating fractals can be an artistic endeavor, a mathematical pursuit, or just a soothing diversion.

Digital art can be purely computer-generated ( such as fractals and algorithmic art ) or taken from other sources, such as a scanned photograph or an image drawn using vector graphics software using a mouse or graphics tablet.

These Lichtenberg figures are considered today to be examples of fractals.

Lichtenberg figures are now known to be examples of fractals.

IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D.

Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.

Physicists have argued over whether fractals can be used to authenticate the paintings.

* Model complexity / diversity: In order to generate visually complex and rich images users of a rendering system need to be free to model large numbers ( 100, 000s ) of complex geometric structures possibly generated using procedural models such as fractals and particle systems.

Small-world networks can also be introduced with time-delay, which will not only produces fractals but also

Another solution sometimes used is algorithmic textures, textures such as fractals that can be generated on-the-fly at arbitrary levels of detail.