A coastline with the stated property is in " a first category of fractals, namely curves whose fractal dimension is greater than 1.

The term " fractal " was first used by mathematician Benoît Mandelbrot in 1975.

Thus, it was not until two centuries had passed that in 1872 Karl Weierstrass presented the first definition of a function with a graph that would today be considered fractal, having the non-intuitive property of being everywhere continuous but nowhere differentiable.

The Sierpinski carpet is a plane fractal first described by Wacław Sierpiński in 1916.

* The term fractal is first used.

This first practical fractal compression system for digital images resembles a vector quantization system using the image itself as the codebook.

The first fractal figures invented near the end of the 19th and early 20th centuries belong to this group.

Fractint was the first widely used fractal generating program.

One of the first exhibitions of fractal art was called Map Art.

Its name comes from the words fractal and integer, since the first versions of it computed fractals by using only integer arithmetic ( also known as fixed-point arithmetic ), which led to much faster rendering on x86 computers without math coprocessors.

In mathematics, the Lévy C curve is a self-similar fractal that was first described and whose differentiability properties were analysed by Ernesto Cesàro in 1906 and G. Farber in 1910, but now bears the name of French mathematician Paul Pierre Lévy, who was the first to describe its self-similarity properties, as well as to provide a geometrical construction showing it as a representative curve in the same class as the Koch curve.

Heisenberg is the first stable fractal biot created by Maximum, and is controlled by Maxwell using a separate remote brain which must be carried around in a case.

At the end of the first movie, " I Worship His Shadow ", the Lexx enters the dark zone through a fractal core located using coordinates found inside one of Stanley Tweedle's teeth.

Repeating this iterative process a large number of times, selecting the vertex at random on each iteration, and throwing out the first few points in the sequence, will often ( but not always ) produce a fractal shape.

Life is further characterized, in antithesis to Piepsam, as animal: the image of a dog, which appears at several places, is first given as the criterion of amiable, irrelevant interest aroused by life considered simply as a spectacle: a dog in a wagon is `` admirable '', `` a pleasure to contemplate '' ; ;

We observe first that no line, l, can meet its image except at one of its intersections with Q.

To do this we must first show that every line which meets **zg in a point P meets its image at P.

When he at last did go to his room, he couldn't sleep and instead paced up and down before his little image of Acala, thinking first of Charlotte's tale of the man at Ryusenji, then of his biwa and the invisible Pacific waters.

The first Abstract Expressionists were considered madmen to give up their brushes and rely on the sheer force of energy to leave an image, but then the import of atomic bombs, all atomic energy, became realized, and art found no better way of expressing its power.

image: Astronaut Harrison ' Jack ' Schmitt, American Flag, and Earth ( Apollo 17 EVA-1 ). jpg | Harrison Schmitt posed with the American flag and Earth in the background during Apollo 17's first EVA.

image: Apollo17UV. jpg | A model of the UV spectrometer used to take the first accurate measurements of the constituents of the Moon's atmosphere.

A vestige of that appears in a portrait of Alexander the Great in a fresco from Pompeii dated to the first century BC, which shows the image of the head of a woman on his armor that resembles the Gorgon.

Two astigmatic image surfaces correspond to one object plane ; and these are in contact at the axis point ; on the one lie the focal lines of the first kind, on the other those of the second.

In 2006 and 2007, J. D. Monnier and his coworkers produced an image of Altair's surface from 2006 infrared observations made with the MIRC instrument on the CHARA array interferometer ; this was the first time the surface of any main-sequence star, apart from the Sun, had been imaged.

This copper-plate engraving from 1795 is the first known image of Brown.

The second player ( B ) plays the mirror image of the first player's move, hoping to divide the board into two pieces and tie the game.

The Challicum bunyip, an outline image of a bunyip carved by Aborigines into the bank of Fiery Creek, near Ararat, Victoria, was first recorded by The Australasian newspaper in 1851.

Bruce then discovers the cavern where he first saw the image that inspired him to become Batman – a giant bat.

Christian Science metaphysics teach that God is Spirit and cites the first chapter of Genesis as the true story of creation, where in the King James Bible, " man " is both " male and female ", created " in the image and likeness " of God.

The discovery image gave the first hint that comet Shoemaker – Levy 9 was an unusual comet, as it appeared to show multiple nuclei in an elongated region about 50 arcseconds long and 10 arcseconds wide.

In 1990 Alston's bust of Martin Luther King, Jr. became the first image of an African American displayed at the White House.

In 1990 Alston's bronze bust of Martin Luther King Jr. ( 1970 ), became the first image of an African American displayed in the White House.

For example, when an ordinary RGB digital image is compressed via the JPEG standard, the RGB colorspace is first converted ( by a rotation matrix ) to a YCbCr colorspace, because the three components in that space have less correlation redundancy and because the chrominance components can then be subsampled by a factor of 2 or 4 to further compress the image.

The dumpster diving term originates from the best-known manufacturer of commercial trash bins, Dempster, who use the trade name " Dumpster " for their bins, and the fanciful image of someone leaping head first into a dumpster as if it were a swimming pool.

A partial solution to this is some programs ' ability to view the composite-order of elements ( such as images, effects, or other attributes ) with a visual diagram called a flowchart to nest compositions, or " comps ," directly into other compositions, thereby adding complexity to the render-order by first compositing layers in the beginning composition, then combining that resultant image with the layered images from the proceeding composition, and so on.

Adelaide Crapsey codified the couplet form into a two line rhymed verse of ten syllables per line with her image couplet poem On Seeing Weather-Beaten Trees, first published in 1915.

Its main competitors were the Bélinograf by Édouard Belin first, then since the 1930s the Hellschreiber, invented in 1929 by German inventor Rudolf Hell, a pioneer in mechanical image scanning and transmission.

The first isomorphism theorem states that the image of any group G under a homomorphism is always isomorphic to a quotient of G. Specifically, the image of G under a homomorphism is isomorphic to where ker ( φ ) denotes the kernel of φ.

But her prettiness was what he had noticed first, and all the other things had come afterward: cruelty, meanness, self-will.

There was an artificial lake just out of sight in the first stand of trees, fed by a half dozen springs that popped out of the ground above the hillside orchard.

The first part of the road was steep, but it leveled off after the second bend and curled gradually into the valley.

No one was behind it, but in the rear wall of the office I noticed, for the first time, a door which had been left partially open.

The herd was watered and then thrown onto a broad grass flat which was to be the first night's bedground.

Once again, Tom Horn was the first and most likely suspect, and he was brought in for questioning immediately.

For Matilda, it was the first she had known in many a night.

Even the knowledge that she was losing another boy, as a mother always does when a marriage is made, did not prevent her from having the first carefree, dreamless sleep that she had known since they dropped down the canyon and into Bear Valley, way, way back there when they were crossing those other mountains.

Stevens was grunting over the last empty pocket when Russ abruptly rose and lunged toward Carmer's hat, which had tumbled half-a-dozen feet away when he first fell.

The Indian's arm whipped sidewise -- there was a flash of amber and froth, the crash of the bottle shattering against the side of the first car.

It was her first smile.

At first, I thought he was out of his head, talking wildly like this.

Hell, I gave him the first decent job he ever had, six, seven -- how many years ago was it, Rob ''??

Miss Langford ( her first name was Evelyn ) was an attractive girl.

School began in August, the hottest part of the year, and for the first few days Miss Langford was very lenient with the children, letting them play a lot and the new ones sort of get acquainted with one another.

It was just as well that the ignorant Dandy enjoyed himself to the hilt that first evening, for the room was to become his prison cell.

`` Bastards '', he would say, `` all I did was put a beat to that Vivaldi stuff, and the first chair clobbered me ''!!

In 1961 the first important legislative victory of the Kennedy Administration came when the principle of national responsibility for local economic distress won out over a `` state's-responsibility '' proposal -- provision was made for payment for unemployment relief by nation-wide taxation rather than by a levy only on those states afflicted with manpower surplus.

The first systematic thinking about this Pandora's box within Pandora's boxes was done four years ago by Fred Ikle, a frail, meek-mannered Swiss-born sociologist.

The smell at first was more surprising than unpleasant.

His collaboration with Washington, begun when he was the general's aide during the Revolution, was resumed when he entered the first Cabinet as Secretary of the Treasury.