Koch snowflake, a fractal that begins with an equilateral triangle and then replaces the middle third of every line segment with a pair of line segments that form an equilateral " bump "

::* Exact self-similarity: identical at all scales ; e. g. Koch snowflake

::* Statistical self-similarity: repeats a pattern stochastically so numerical or statistical measures are preserved across scales ; e. g., randomly generated fractals ; the well-known example of the coastline of Britain, for which one would not expect to find a segment scaled and repeated as neatly as the repeated unit that defines, for example, the Koch snowflake

:* Iterated function systems – use fixed geometric replacement rules ; may be stochastic or deterministic ; e. g., Koch snowflake, Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Harter-Heighway dragon curve, T-Square, Menger sponge

For instance, a side of the Koch snowflake is both symmetrical and scale-invariant ; it can be continually magnified 3x without changing shape.

Moore compares the multitude of increasingly outlandish Ripper theories to a Koch snowflake, where a finite, fixed location, event and era ( London, in late 1888 ) can have an infinite number of nooks and crannies.

The first four iteration s of the Koch snowflake

The Koch snowflake ( also known as the Koch star and Koch island ) is a mathematical curve and one of the earliest fractal curves to have been described.

The Koch snowflake is the limit approached as the above steps are followed over and over again.

In other words, three Koch curves make a Koch snowflake.

So the area of a Koch snowflake is 8 / 5 of the area of the original triangle, or.

Tesselation by two sizes of Koch snowflake

Since each Koch snowflake in the tesselation can be subdivided into seven smaller snowflakes of two different sizes, it is also possible to find tessellations that use more than two sizes at once.

the resulting curve converges to the Koch snowflake.

The image of simple plane curve can have Hausdorff dimension bigger than one ( see Koch snowflake ) and even positive Lebesgue measure ( the last example can be obtained by small variation of the Peano curve construction ).

Niels Fabian Helge von Koch ( Stockholm, January 25, 1870 – ibidem, March 11, 1924 ) was a Swedish mathematician who gave his name to the famous fractal known as the Koch snowflake, one of the earliest fractal curves to be described.

* Koch snowflake

One non-trivial example is the fractal dimension of a Koch snowflake.

* Koch snowflake

* Helge von Koch describes the " Koch snowflake ", one of the earliest fractal curves described.

A hagiographic account of Koch's career can be found in the 1939 Nazi propaganda film Robert Koch, der Bekämpfer des Todes ( The fighter against death ), directed by Hans Steinhoff and starring Emil Jannings as Koch.

In 1876, Robert Koch ( 1843 – 1910 ) established that microbes can cause disease.

More specifically, Helge von Koch showed in 1901 that, if and only if the Riemann hypothesis is true, the error term in the above relation can be improved to

Further influence of A. M. Cassandre and Rudolf Koch, whose work greatly inspired the young Zapf, can also be seen in Optima.

The Koch Curve can be expressed by a rewrite system ( Lindenmayer system ).

In the " Individual Notes on Works and Authors " in the " Special Collaborations Issue " of Locus Solus, Kenneth Koch wrote, " Though Harris was wrong about who Ern Malley ' was ' ( if one can use that word here ), I find it hard not to agree with his judgment of Malley's poetry.

He once remarked that “ Maybe you can almost characterize the poetry of the New York School as having as one of its main subjects the fullness and richness of life and the richness of possibility and excitement and happiness .” In his poem The Art of Poetry ( 1975 ) Koch offered guidelines to writing good poetry.

Apart from these, more recently as a part of greater Northeast India, state of Sikkim and parts of North Bengal ( districts of Darjeeling, Jalpaiguri, and Koch Bihar ) can also be collectively referred as Northeast India.

Thus, for example the Koch curve scales with, but the scaling holds only for values of for integer n. In addition, the Koch curve scales not only at the origin, but, in a certain sense, " everywhere ": miniature copies of itself can be found all along the curve.

While experimenting on chimpanzees in Kindia, on whom he was able to test exhaustively his vaccine, Calmette also discovered that it can notably weaken some leprosy-its bacillus presents some similarities with Koch ’ s one-manifestations.

Koch himself believes that a considerable part of the poem can be dated to the 6th century.

Other firearms, such as the Beretta 70 / 90 assult weapons system, Heckler & Koch MP5 sub-machine guns and Benelli shotguns are in service with the corps and can either be issued to the general personnel according to particular necessities or to the specialties the officers are assigned to.

Some airsoft guns can be such accurate replicas that they violate intellectual property laws ( specifically those regarding trademarks ), most notably some models from Tokyo Marui bearing Colt or Heckler & Koch trademarks that may not be imported into the United States.

In addition, to show that a microorganism causes the disorder, the Koch postulates would require one show that the organism is present in all cases of the disorder, that the organism can be extracted from those with the disorder and be cultured, that transferring the organism into healthy subjects causes the disorder, and the organism can be reisolated from the infected party.

The Tartessian language from the southwest of the Iberian peninsula, written in a version of the Phoenician script in use around 825 BC, which John T. Koch has claimed to be able to readily translate, has been accepted by a number of philologists and other linguists as the first attested Celtic language, but the linguistic mainstream continues to treat Tartessian as an unclassified ( Pre-Indo-European?

Koch was unaware of Pacini's work and made an independent discovery, and his greater preeminence allowed the discovery to be widely spread for the benefit of others.

be: Heckler & Koch

One way of proving that a given disease is " infectious ", is to satisfy Koch's postulates ( first proposed by Robert Koch ), which demands that the infectious agent be identified only in patients and not in healthy controls, and that patients who contract the agent also develop the disease.

Likewise, the German Heckler & Koch MP5K ( a weapon small enough to be concealed on one's person or in a briefcase ), is also classed as a compact submachine gun.

The Heckler & Koch G3 battle rifles used were considered by several experts to be inadequate for the distance at which the snipers were trying to shoot.

One type of broad usage would later be narrowed down by Koch in 1891 to the ' psychopathic inferiorities ' - later renamed abnormal personalities by Schneider.

Revisiting the film in his 1976 article " Fashions in Pornography " for Harper's Magazine, Stephen Koch found its sadistic violence to be extreme and unimaginative.

** Dutch painter Han van Meegeren is arrested for collaboration with the Nazis, but the paintings he had sold to Hermann Göring ( Koch ) are later found to be his fakes.

After a short tour of the United States, where he visited Hollywood, he returned to Italy to be Renoir's assistant again, this time for La Tosca ( 1939 ), a production that was interrupted and later completed by German director Karl Koch because of World War II.

More than 1, 500 places were ordered to be renamed by 16 July 1938 following a decree issued by gauleiter and Oberpräsident Erich Koch and initiated by Adolf Hitler.

Josias investigated the case and found out that Koch, in a position as the Camp Commandant, had ordered Krämer and Karl Peixof, a hospital attendant, killed as " political prisoners " because they had treated him for syphilis and he feared it might be discovered.

Although this skin had not been fashioned into a lampshade, US prosecutor Thomas Dodd claimed that Ilse Koch had ordered tattooed human skin to be made into lampshades for her home.

According to Koch, the name Arawn may be derived from the Biblical name Aaron, the name of Moses ’ s brother, and so is ultimately of Hebrew origin and meaning ‘ exalted .’ That the name ‘ Aaron ’ had currency in Wales as early as Roman times is shown by Gildas who wrote that ‘ Aaron and Iulianus were Christian martyrs at Urbs Legionis ( the ‘ city of the legion ,’ probably Caerllion-ar-Wysg ) in the time of the Emperor Diocletian .’ a cleric of the Old Welsh name Araun witnessed two charters of 860 preserved in the book of Llandaf.

On August 3, 1946, retired industrialist Louis J. Koch opened Santa Claus Land, which is claimed to be the world's first theme park.