Showing posts with label fractals. Show all posts
Showing posts with label fractals. Show all posts

Saturday, January 21, 2012

Louis Wain (5 August 1860 – 4 July 1939)

The British artist Louis Wain was a highly successful illustrator whose reputation was made on his singular and gently humorous pictures of cats. A cat-lover himself and sometime President of The National Cat Club, Wain claimed in an interview in 1896 that his "fanciful cat creations" were first suggested to him by Peter, his black & white cat. Demand for Wain's work diminished in the decade after the outbreak of the First World War, leaving him progressively impoverished. He began to show signs of mental disorder, including becoming aggressive,babusive and sometimes violent.
In 1924 he was certified insane and placed in the paupers' ward of Springfield Hospital at Tooting. Despite his delusional state, Wain continued to draw and paint, which led a year later to him being recognised by one of the hospital guardians and transferred to a private roomat the Royal Bethlem Hospital in Southwark, with money raised through public appeal.
In Bethlem he was allowed to draw as much as he liked, and it was here that he produced the first of his facinating series of "kaleidoscope" cats. These ranged from relatively straightforward renderings of the cat itself, though painted in intense, non-naturalistic colour and surrounded by intricate geometric patterns which deny any illusion of spatial depth, to images in which the figure of the cat is exploded in a burst of geometric fragments, the like of which are not to be found in any of Wain's work before his illness. In 1930he was moved to Napsbury in Hertfordshire, where he continued to work sporadically until his death in 1939.

Found Here: http://www.outsiderart.co.uk/wain.htm


From this point, Wain's popularity began to decline. He returned from New York broke, and his mother had died of Spanish Influenza while he was abroad. His mental instability also began around this time, and increased gradually over the years. He had always been considered quite charming, but odd, and often had difficulty in distinguishing between fact and fantasy. Others frequently found him incomprehensible, due to his way of speaking tangentially. His behaviour and personality changed, and he began to suffer from delusions, with the onset of schizophrenia. Whereas he had been a mild-mannered and trusting man, he became hostile and suspicious, particularly towards his sisters. He claimed that the flickering of the cinema screen had robbed the electricity from their brains. He began wandering the streets at night, rearranging furniture within the house, and spent long periods locked in his room, writing incoherently.
Some speculate that the onset of Wain's schizophrenia was precipitated by toxoplasmosis, a parasitic infection that can be contracted from cats. The theory that toxoplasmosis can trigger schizophrenia is the subject of ongoing research, though the origins of the theory can be traced back as early as 1953.[3][4][5][6]
When his sisters could no longer cope with his erratic and occasionally violent behavior, he was finally committed, in 1924, to a pauper ward of Springfield Mental Hospital in Tooting. A year later, he was discovered there and his circumstances were widely publicized, leading to appeals from such figures as H. G. Wells and the personal intervention of the Prime Minister. Wain was transferred to the Bethlem Royal Hospital in Southwark, and again in 1930 to Napsbury Hospital near St Albans in Hertfordshire, north of London. This hospital was relatively pleasant, with a garden and colony of cats, and he spent his final 15 years there in peace. While he became increasingly deluded, his erratic mood swings subsided, and he continued drawing for pleasure. His work from this period is marked by bright colours, flowers, and intricate and abstract patterns, though his primary subject remained the same.

Dr. Michael Fitzgerald disputes the claim of schizophrenia, indicating Wain more than likely had Asperger's Syndrome (AS). Of particular note, Fitzgerald indicates that while Wain's art took on a more abstract nature as he grew older, his technique and skill as a painter did not diminish, as one would expect from a schizophrenic.[7] Moreover, elements of visual agnosia are demonstrated in his painting, a key element in some cases of AS. If Wain had visual agnosia, it might have manifested itself merely as an extreme attention to detail.[8]
A series of five of his paintings is commonly used as an example in psychology textbooks to putatively show the change in his style as his psychological condition deteriorated. However, it is not known if these works were created in the order usually presented, as Wain did not date them. Rodney Dale, author of Louis Wain: The Man Who Drew Cats, has criticised the belief that the five paintings can be used as an example of Wain's deteriorating mental health, writing: "Wain experimented with patterns and cats, and even quite late in life was still producing conventional cat pictures, perhaps 10 years after his [supposedly] 'later' productions which are patterns rather than cats."[9]
H. G. Wells said of him, "He has made the cat his own. He invented a cat style, a cat society, a whole cat world. English cats that do not look and live like Louis Wain cats are ashamed of themselves."
His work is now highly collectible but care is needed as forgeries are common.

Found Here: http://en.wikipedia.org/wiki/Louis_Wain


Louis Wain was born in the Clerkenwell district in London and became an artist, selling his sketches of dog shows to the Illustrated Sporting News. He married his youngest sister's governess, Emily Richardson, which caused quite a scandal. Unfortunately, his wife fell ill with breast cancer and died three years later. To entertain her on her sickbed, Louis Wain started drawing their cat, Peter.

Emily encouraged him to send these drawings to newspapers and magazines, and soon the Louis Wain cat was a household name, not only in Britain but also in America, where his comics and drawings of cats appeared in several newspapers. Louis Wain was elected as President of the National Cat Club and wrote the book 'In Animal Land with Louis Wain' in 1904.

After the First World War, the public's interest in cats diminished, and Wain reached a personal crisis, falling into poverty and being affected by schizophrenia when he was 57 years old. In 1924, he was certified insane and admitted to the pauper's wing of a mental hospital in Tooting.

Years later, he was recognized and a fund was set up for him (by prominents such as H.G. Wells), enabling Louis Wain to spent his last years, until his death in 1939, in comfortable asylums in Southwark and Napsbury, where he continued to draw and paint cats.

Found Here: http://lambiek.net/artists/w/wain_louis.htm

Among other things, the British artist Louis Wain (1860-1939) painted cats. Although he had formally studied at the West London School of Art and specialized in animal paintings and nature scenes, the cat paintings which would eventually define him began to spring from his brush soon after his marriage in 1883 – his wife was diagnosed with cancer soon after their nuptials, and during the period of illness, she being much comforted by cats, he began to paint cats for her in a comic and anthropomorphic style, until the time of her death, only three years after their marriage.

He continued painting cats after her death, but as the years progressed, his “style” began to change, even as his normally gentle personality transformed into a hostile and paranoid one. This was around the year 1907, and given his age at this time (47), as well as the fact that he seemed to have become profoundly mentally ill at this time, it is widely supposed that he must have been the victim of an atypical, late-onset schizophrenia (schizophrenia usually develops in the late teens and early twenties). Due his close association with cats and a probable infection with toxoplasmosis, which can be acquired from cat feces, a link between toxoplasmosis and schizophrenia has been suggested, but no definitive link has been established, to date. Other authorities have disputed that he had schizophrenia at all, because a diminishment of style often results in artists who develop the disease, and Wain’s art, while increasingly bizarre in appearance, retained its technically competent character.

Asperger’s Syndrome – a form of autism – has been suggested, and this would help explain a certain “eccentricity” and oddness of manner and speech he had possessed much of his life.

Whatever the case, as Wain’s “illness” progressed, his paintings became increasingly bizarre and abstracted in appearance, to the point where they were almost frightening, and often not even recognizable as cats. His work is commonly shown as a progression, to illustrate the changes, as I have done below.

Found Here: http://rodscuriosityshop.wordpress.com/2011/05/13/the-curious-cats-of-louis-wain/

Tuesday, November 16, 2010

Burning Ship fractal




The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E. Rössler in 1992, is generated by iterating the function:

z_{n+1} = (|\operatorname{Re} \left(z_n\right)|+i|\operatorname{Im} \left(z_n\right)|)^2 + c, \quad z_0=0

in the complex plane \mathbb{C} which will either escape or remain bounded. The difference between this calculation and that for the Mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy–Riemann conditions.[1]


  1. ^ Michael Michelitsch and Otto E. Rössler (1992). "The "Burning Ship" and Its Quasi-Julia Sets". In: Computers & Graphics Vol. 16, No. 4, pp. 435–438, 1992. Reprinted in Clifford A. Pickover Ed. (1998). Chaos and Fractals: A Computer Graphical Journey — A 10 Year Compilation of Advanced Research. Amsterdam, Netherlands: Elsevier. ISBN 0-444-50002-2
Found Here: http://en.wikipedia.org/wiki/Burning_Ship_fractal

The images described here are generated by analysing the following series for each point (cx,cy) on the plane.

The grey level assigned to each point (cx,cy) is determined by how fast the series tends to infinity. For example, the points shown in black in the center of the form don't ever diverge to infinity. The points shown in light grey diverge very quickly. This is exactly the same technique used to create the Mandelbrot image. In all cases the starting point (x0,y0) is (0,0).

This fractal gets its name from the images obtained by zooming into regions along y=0 (x axis) an example is shown below

Source code

This C source code gives the basic idea of how the images on this page were created. As it stands it is run given a centre coordinate, a image width in world coordinates, and the name of the output file. It writes a raw RGB or greyscale image, this can be opened with most image editors or you can modify the code to save the image in your favorite format.

Found Here: http://local.wasp.uwa.edu.au/~pbourke/fractals/burnship/

Saturday, October 24, 2009

Fractals

A fractal 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,"[1] a property called self-similarity. Roots of mathematical interest in fractals can be traced back to the late 19th Century; however, the term "fractal" was coined by Benoît Mandelbrot in 1975 and was derived from the Latinfractus meaning "broken" or "fractured." A mathematical fractal is based on an equation that undergoes iteration, a form of feedback based on recursion.[2]

A fractal often has the following features:[3]

Because they appear similar at all levels of magnification, fractals are often considered to be infinitely complex (in informal terms). Natural objects that approximate fractals to a degree include clouds, mountain ranges, lightning bolts, coastlines, snow flakes, various vegetables (cauliflower and broccoli), and animal coloration patterns. However, not all self-similar objects are fractals—for example, the real line (a straight Euclidean line) is formally self-similar but fails to have other fractal characteristics; for instance, it is regular enough to be described in Euclidean terms.

Images of fractals can be created using fractal-generating software. Images produced by such software are normally referred to as being fractals even if they do not have the above characteristics, as it is possible to zoom into a region of the image that does not exhibit any fractal properties.

Thursday, June 25, 2009

Fossilized Algae

Stromatolites (from Greek στρώμα, strōma, mattress, bed, stratum, and λιθος, lithos, rock) are layered accretionary structures formed in shallow water by the trapping, binding and cementation of sedimentary grains by biofilms of microorganisms, especially cyanobacteria (commonly known as blue-green algae). They are the oldest living organisms on the planet, and are believed to be the first living organisms on Earth.[1]

Earth’s oldest fossils are the stromatolites consisting of rock built from layer upon layer of sediment and other precipitants.[3] Based on studies of now-rare (but living) stromatolites (specifically, certain blue-green bacteria), the growth of fossil stromatolitic structures was biogenetically mediated by mats of microorganisms through their entrapment of sediments. However, abiotic mechanisms for stromatolitic growth are also known, leading to a decades-long and sometimes-contentious scientific debate regarding biogenesis of certain formations, especially those from the lower to middle Archaean eon.

It is most widely accepted that stromatolites from the late Archaean and through the middle Proterozoic eon were mostly formed by massive colonies of cyanobacteria (formerly known as blue-green "algae"), and that the oxygen byproduct of their photosynthetic metabolism first resulted in earth’s massive banded iron formations and subsequently oxygenated earth’s atmosphere.

Even though it is extremely rare, microstructures resembling cells are sometimes found within stromatolites; but these are also the source of scientific contention. The Gunflint Chert contains abundant microfossils widely accepted as a diverse consortium of 2.0 Ga microbes.[4]

In contrast, putative fossil cyanobacteria cells from the 3.4 Ga Warrawoona Group in Western Australia are in dispute since abiotic processes cannot be ruled out.[5] Confirmation of the Warrawoona microstructures as cyanobacteria would profoundly impact our understanding of when and how early life diversified, pushing important evolutionary milestones further back in time (reference). The continued study of these oldest fossils is paramount to calibrate complementary molecular phylogenetics models.

Cyanobacteria Relationship to Earth's History
The biochemical capacity to use water as the source for electrons in photosynthesis evolved once, in a common ancestor of extant cyanobacteria. The geologic record indicates that this transforming event took place early in our planet's history, at least 2450-2320 million years ago (mya), and probably much earlier. Geobiological interpretation of Archean (>2500 mya) sedimentary rocks remains a challenge; available evidence indicates that life existed 3500 mya, but the question of when oxygenic photosynthesis evolved continues to engender debate and research. A clear paleontological window on cyanobacterial evolution opened about 2000 mya, revealing an already diverse biota of blue-greens. Cyanobacteria remained principal primary producers throughout the Proterozoic Eon (2500-543 mya), in part because the redox structure of the oceans favored photautotrophs capable of nitrogen fixation. Green algae joined blue-greens as major primary producers on continental shelves near the end of the Proterozoic, but only with the Mesozoic (251-65 mya) radiations of dinoflagellates, coccolithophorids, and diatoms did primary production in marine shelf waters take modern form. The most common cyanobacterial structures in the fossil record include stromatolites and oncolites. Cyanobacteria remain critical to marine ecosystems as primary producers in oceanic gyres, as agents of biological nitrogen fixation, and, in modified form, as the plastids of marine algae.[10]