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*Fractals*

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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 dimension, 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 infinite 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 compress 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.

- Chaostheory
- "as above, so below" - occult maxim
- Udo of Aachen - monk from 1200-1270 CE, and his discovery of the Mandelbrot Set

There are points in _Writing
On Drugs_ where Sadie Plant flirts with
the idea that drugs can access certain "revelations." The twist
is that it's not a transcendent reality "out
there," but one deep within the hard wiring 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 psychedelic
experience through history and across the globe. The deranged geometry
of lattices, honeycombs, lacework, and
spiderwebbing, the baroquely infolding spirals and proliferating
ornamentation, and the mosaic vision
and kaleidoscopic turbulence, seen by users of LSD, peyote, DMT, psilocybin,
and other hallucinogens, find a
visual echo in such cultural forms as the "coptic light"
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 MS/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.

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 singularity,
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 moment
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 light
of day, then the game cannot continue.

-Terence
McKenna - _Live at Wetlands Preserve, NYC July 28, 1998_

Devised by Benoit Mandelbrot from the adjective
latin term Fractus, from the verb Frangere, to break. Theresonance
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 chaos.
"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. Leibniz
imagined that a drop of water 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 process 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 information.
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 ClockDVA
off of _Man-Amplified_ CD on Contempo (1992)

The final crop
circle formation of 1997, was the "Strange
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 Terence McKenna
to describe the "Omega Point," which sucks
our evolutionary trajectory towards it, like
the plughole at the end of time.

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 offlow. Even literary theory is now surfing the fractal edge.

- Erik Davis - _Lost In Hyperspace_

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 foundations 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 dimension**

"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."

Crop Circle,
Mandelbrot Set 1991 at Ickleton, south of Cambridge |

- Mandelbrot set
- experimental rock instrumental track _Klein Mandelbrot_ MP3 (vK) by Blue Man Group off of _Audio_ (1999)
- lo fi entity Julia set
- lo-fi track _Battery_ MP3 by The Julia Sets off of _The Last 100 Days Of..._ 12"
- lo-fi track _Domino_ MP3 by The Julia Sets off of 7"
- track _Fractal Zoom_ MP3 (160k) by Brian Eno off of _Nerve Net_ (1992)
- release _Fractal Zoom_ CDS by Brian Eno on Opal/(1992)

- (separate time edit)
- (mary's birthday edit)
- (up river mix)
- (small country)
- the roil, the choke
- fractal zoom (naive mix I)
- (zaire mix)
- (naive mix II)
- (landed mix)
- (bucolic mix)
- (separate time full length)
- (mary's birthday mix)
- data compression (e.g. pkzip) as fractals

- release _Fractal Flow_ by Silver Apples (1996)

- IDM breaks track _Fractical Practal_ MP3 (vK) by Smyglyssna off of _We Can Fix It_ CD on Vertical Form #015 (2002)
- abstract trip hop release _Fractal Abstraction_ CD by Goo on Shadow (2000)
- 604 entity Fractal Glider
- track _The Shepherd_
- release _Parasite_ CD on Boom!
- 604 track _Fractal Gates_ by Etnica
- 604 track _Ghost In The Shell_ by Fractal & Benza
- techno track _Fractal_ MP3 (192k) by Marco Bailey off of _Simply Techno_ 12" on Virus #1 (1999)
- Fractal System

^{Fractal System - _Scary Song (Alex Mind Remix)_} |

- techno release _Micro MP3 (192k)/Macro_ MP3 (192k) 12" by D-Ex vs. Marco Lenzi on Molecular (1998)
- math rock track _Big Things, Little Things_ MP3 (192k) by Rodan off of _Peel Session_ (1994)
- illbient drill & bass track _These Structures Are Uneven_ MP3 by Weakener off of _Suffocate_ CDr on Stank Sound #002 (2000)
- track _Fractal_ MP3 (192k) by Shapes & Forms off of s/t CD on k2o (2001)
- IDM breaks track _Fractical Practal_ MP3 (vK) by Smyglyssna off of _We Can Fix It_ CD on Vertical Form #015 (2002)
- cinematic IDM track _Scaling_ Mp3 (160k) by u-Ziq off of _Royal Astronomy_ CD on Hut Recordings #055 (1999)
- track _The Devil Is In The Details_ MP3 (192k) by Boards Of Canada off of _Geogaddi_ CD on Warp (2002)
- track _Worlds Within
Worlds_ MP3 (192k)(ed2k192k)
**by Cylob off of _Mood Bells_ CD on EFA (2002)** - track _Wiggly World_ by Devo off of _Duty Now For The Future_ 12" on Warner Brothers 1979