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fractals...

Fractals
This nOde last updated December 17th, 2004 and is permanently morphing...
(3 Ix (Jaguar) / 17 Mac - 94/260 - 12.19.11.15.14)

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fractal

fractal (fràk´tel) noun
A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature.

[French, from Latin frâctus, past participle of frangere, to break.]

Fractal

Fractal, any of many geometric shapes that are complex and detailed at any scale. Fractals are often self-similar- that is, each portion is a reduced-scale replica of the whole. Many such self-repeating figures can be constructed.

French mathematician Benoit B. Mandelbrot discovered fractal geometry in the 1970s. Mandelbrot adopted an abstract definition of internal linkdimension, with the result that a fractal cannot be treated mathematically as existing in one, two, or any other whole-number dimensions. It must be treated as having some fractional dimension.

A coastline, if measured at progressively smaller scales, would tend toward internal linkinfinite length. Mandelbrot has suggested that mountains, clouds, galaxy clusters, and other natural phenomena are similarly fractal in nature. The beauty of fractals has made them a key element in computer graphics. Fractals have also been used to internal linkcompress still and video images in a variety of multimedia and other image-based computer applications.

fractal

fractal (frak'tel) noun
A word coined by mathematician Benoit Mandelbrot in 1975 to describe a class of shapes characterized by irregularity, but in a way that evokes a pattern. Computer graphics technicians often use fractals to generate naturelike images such as landscapes, clouds, and forests. The distinguishing characteristic of fractals is that they are "self-similar"; any piece of a fractal, when magnified, has the same character as the whole. The standard analogy is that of a coastline, which has a similar structure whether one is looking at the coastline of a state or that of a continent. Interestingly, it is often difficult to measure the length of the perimeter of such a shape exactly because the total distance measured depends on the size of the smallest element measured. For example, one could measure on a given coastline the perimeter of every peninsula and inlet, or at a higher magnification the perimeter of every small promontory and jetty, and so on. In fact, a given fractal may have a finite area but an infinite perimeter; such shapes are considered to have a fractional dimension- for example, between 1 (a line) and 2 (a plane)- hence the name fractal.


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boundary dissolution...

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There are points in _Writing On Drugs_ where internal linkSadie Plant flirts with the idea that drugs can access certain "revelations."  The internal linktwist is that it's not a transcendent internal linkreality "out there," but one deep within the hard internal linkwiring of the brain itself. She subscribes to Henri Michaux's mescaline-inspired conviction that there's a kind of pre-cultural commonality underlying all the many forms of internal linkpsychedelic experience through history and across the globe. The deranged geometry of lattices, internal linkhoneycombs, lacework, and spiderwebbing, the baroquely infolding spirals and proliferating ornamentation, and the internal linkmosaic vision and  kaleidoscopic turbulence, seen by users of internal linkLSD, internal linkpeyote, internal linkDMT, internal linkpsilocybin, and other internal linkhallucinogens, find a visual echo in such cultural forms as the "coptic internal linklight" patterns of Arabian carpets and the paisley fabric of the Indian subcontinent. Michaux speculated that all this drug-induced eye candy constitutes an amplification of  brain wave activity, especially that of the visual cortex. The fact that some migraine sufferers see similar patterns --  known as the migraine aura -- suggests that in certain extreme states, the internal linkMS/DOS and subroutines of the brain can be apprehended by consciousness. "Some people can  get the aura effects without the pain of migraine," says Plant. "It's happened to me about three times in my life,  at times of extreme exhaustion. This almost kaleidoscopic stuff kind of creeps across your visual field from one side  to the other. It's really quite stunning, and not at all scary.  The fact that there are 'natural' equivalents to drug-induced experiences suggests the possibility you are in some sense observing what's going on in the brain." Noting the similarity between these psychedelic hallucinations and the self-similar patterns of Mandelbrot's fractals, Plant characterizes the drugged or migrained brain as a cranked-up biochemical computer capable of picturing the self-organizing behavior and nonlinear dynamism at play within normally staid reality.
 

LSD Peyote

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So I think about all of this all the time, and I feel great change. I try to monitor it, especially in the realm of society and technology.  Everything is redefined every 30 days, every 60 days, redefined toward some kind of internal linksingularity, some kind of extra-ordinary moment in the fractal pattern of Historical unfoldment. You know, fractals are always repetitious, always low levels build to higher levels, but nevertheless, intrinsically to the pattern, there comes a internal linkmoment where there is an apotheosis, a breakthrough to a new level of understanding. And then whatever the old world was, it simply dissipates. It goes away.  Not that there isn't political struggle, but once the (let's call it) karmic underpinnings of a historical position -- especially an oppressive historical position -- once those underpinnings are articulated, revealed, shown in the internal linklight of day, then the game cannot continue.
 -internal linkTerence McKenna - _Live at Wetlands Preserve, NYC July 28, 1998_ 

Singularity Terence McKenna

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Devised by Benoit Mandelbrot from the adjective latin term Fractus, from the verb Frangere, to break.  Theinternal linkresonance of the main English cognates - Fracture and Fraction (noun and adjective (English and French)).  Mandelbrot devised the word Fractal to describe a new mathematical geometry, part of the new science of internal linkchaosHail Eris!.  "A fractal is a geometric shape, a geometric shape having a special property that as you look closer and closer to it you see it is essentially the same thing."  The notion of self-similarity strikes ancient chords in our culture.  An old strain in western thought honors the idea. internal linkLeibniz imagined that a drop of internal linkwater contained a whole teeming universe containing in turn waterdrops and new universes within.  "To see the world in a grain of sand." - Blake. When spermatozoa was first discovered it was thought to be an homunculus, a human, tiny, but fully formed.  But self-similarity receded as a scientific principle, and the internal linkprocess of ontogenetic development is far more interesting than mere enlargement.  The myth died hard as the human vision was extended by telescopes and microscopes.  The first discoveries were realizations taht each change of scale brought new phenomena and new kinds of behavior.  For modern particle physicists, the process has never eneded.  Every new accelerator with its increase in energy and speed, extends sciences field of view to tinier particles and briefer time scales and every extension seems to bring new internal linkinformation.  But physicists wanted to know more.  They wanted to know why.  There were forms in nature, not visible forms, but shapes embedded in the fabric of motion, waiting to be revealed.
- from the liner notes of track _Fractalize_ by internal linkClockDVA off of _Man-Amplified_ CDatomjacked inventory cache on Contempo (1992)

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Kilroy Was Here fractals

 


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The final internal linkcrop circle formation of 1997, was the "internal linkStrange Attractor" fractal at Hackpen Hill .   The term means "an irreducible invariant set that attracts the trajectories of all nearby points." This term was used by internal linkTerence McKenna to describe the "internal linkOmega Point," which sucks our internal linkevolutionary trajectory towards it, like the plughole at the end of internal linktime.
  

Strange Attractor Crop Circle - Koch Snowflake Fractal Omega - The End

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In recent years, chaos has migrated from mathematics, physics, and computer science departments to fields as far off as anthropology and economics, displaying a viral panache similar to poststructuralism's as it spread through the humanities. And perhaps it's no mere coincidence. In "Non-Organic Life," an article in Zone Incorporations,  Manuel DeLanda persuasively links the chaotic process of self-organization with Deleuzian poststructuralism, suggesting a more-than-metaphoric link between natural and social formations and sketching out a potent ethics ofinternal linkflow. Even literary theory is now surfing the fractal edge.

- Erik Davis - _Lost In internal linkHyperspace_


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WHEN COSMOLOGISTS SPECULATE on the nature of the Universe, they make an unspoken assumption--that matter is spread uniformly throughout space. Yet when astronomers peer out across the Universe they see something very different.

Galaxies are gathered together in great chains and walls which snake around vast regions of empty space called voids.

The Universe appears anything but uniform.

"Yes, there does appear to be a contradiction," admits Ofer Lahav of the Hebrew University in Jerusalem and the Institute of Astronomy in Cambridge. But Lahav contends that the Universe, though undeniably clumpy on the small scale, becomes smooth on the largest scales. "I like to think of it as an ocean, which looks choppy on the scale of individual waves but from far above, on scale of tens of kilometres, is perfectly smooth," he says.

A maverick group based in Europe has suggested that the Universe never becomes smoothed out, even on the largest scales. "My contention is that it is clumpy on all the scales so far explored," says Francesco Sylos Labini, an astronomer at the University of Geneva. "In fact, studies we have done show that the distribution of matter is fractal, just like a tree or a cloud."

If this dissenting view is correct and the Universe doesn't become smoothed out on the very largest scales, the consequences for cosmology are profound. "We're lost," says Coles. "The internal linkfoundations of the big bang models would crumble away.

We'd be left with no explanation for the big bang, or galaxy formation, or the distribution of galaxies in the Universe."

Fractal internal linkdimension

"Our tests show that the Universe never becomes homogeneous in the available galaxy samples," says Sylos Labini, who began his work while in Pietronero's team.

"It remains hierarchically clustered. It remains fractal."

"If the Universe is fractal, however, it has no characteristic scale," says Sylos Labini. "Everything, including the average density, changes with scale so the concept is meaningless.

It's not surprising that people find the Universe is homogeneous when homogeneity is one of their basic assumptions."

Despite this formidable theoretical challenges, Sylos Labini believes a fractal Universe is more exciting than a homogeneous one. "We are facing a new and challenging problem which we are a long way from solving," he says. "For some questions, the fractal structure leads to a radically new perspective and this is hard to accept. But it is based on the best data and analyses available. It is neither a conjecture nor a model--it is a fact."


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Crop Circle - Mandelbrot Set 1991 at Ickleton, south of Cambridge
internal linkCrop Circle, Mandelbrot Set 1991 at Ickleton, south of Cambridge


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Devo - Duty Now For The Future Cylob - Mood Bells on EFA (2002)
Smyglyssna - We Can Fix It CD on Vertical Form (2002) Goo - Fractal Abstraction by Goo on Shadow (2000)

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internal linkUsenet: sci.fractals

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