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lg_APT22A.jpg A Planetary Sit-in	lg_CC01010A.jpg Here Is What You Asked For	lg_CC01010C.jpg The small i am
lg_CC01010D.jpg Field Merchant	lg_Div8001j.jpg The Wicker of Ritual	lg_R000103Y.jpg Feeling Wild
lg_R000106z.jpg Dancer	lg_R000109F.jpg New Symbolic	lg_R000112C.jpg Smooth
lg_R000121A.jpg Helpless	lg_R000121D.jpg Seasons That Leave Out The Storms	lg_R000127Q.jpg Your Demons Spoke To Me
lg_R000128a.jpg I No Longer Worried	lg_R000136J.jpg This Is Where It Lasts	lg_R000136M.jpg A Captivating Audience
lg_R000136R.jpg We Go Beyond The End	lg_R000136W.jpg Higher Planes Will Seize You	lg_R000137e.jpg I Don't Know Anything Anymore
lg_R000138K.jpg Are You Heaven Sent?	lg_R000138N.jpg I Remembered A Voice	lg_R000138P.jpg It Formed Before These Eyes
lg_R000139C.jpg A Twist of Youth	lg_R000139O.jpg A Coming Together of Like Minds	lg_R000139R.jpg The Cosmos Celebrates Your Coming Of Age
lg_R000140A.jpg Eyes To See You	lg_R000140C.jpg Too Many Folds To Unravel	lg_R000140D.jpg The Magnificent Beyond
lg_R000140E.jpg A Candle Without Its Breeze	lg_R000140F.jpg Whiplash	lg_R000140I.jpg Stars Are Forming
lg_R000140N.jpg How Can I Know You?	lg_R000140O.jpg All Lined Up	lg_R000140P.jpg We Were Stronger Than Our Need

lg_R000141A.jpg All Safe From Where You Left Off	lg_R000141B.jpg Are You Happy In Your Derision?	lg_R000152E.jpg A Crown Without A Ruler
lg_R001100E.jpg In Conjunction	lg_R981201I.jpg A Flicker Of Memory and Meaning	lg_R981205A.jpg A Force Of Converging Energy
lg_R981208S.jpg The Wizard	lg_R990403S.jpg Hearing Aid	lg_R990925E.jpg The Evolutionaries
lg_T001102M.jpg Power As In Kraft	lg_T001104V.jpg A Catepillar of Consequence	lg_T001106D.jpg Don't Fight the Demons Who Are Misunderstood
lg_te0101r2.jpg A Standard Nebula	lg_te00011n.jpg Golden Handling	lg_te00012h.jpg A Claw Without A Hand
lg_te00012o.jpg Homogenous	lg_te36001d.jpg Re-formation And Moving On	lg_TE99093M.jpg The Emerging
lg_TE99093N.jpg Heroes Of Thought Flight	lg_TE99095S.jpg Keep-safe	lg_Z010102K.jpg Cauliflower Flare
lg_Z010103I.jpg Hall of Ralf und Florian	lg_Z010103Z.jpg A Meeting Of Minors	lg_Z010105Z.jpg The Always Wanted
lg_Z010106L.jpg A Pleasure To Be You	lg_Z010107G.jpg Microcondrial DNA	lg_Z010107I.jpg Isthmus
lg_Z010107J.jpg Field Descriptor	lg_Z010108B.jpg A Halo in My Motor Oil	lg_Z010108D.jpg Divinity Agent

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Keywords: periodic loop iteration. Complex numbers imaginary component random formula parameters . Complex plane universe self-similar and self similarity algebra julia ikenaga newton tetration tilemandel koch sierpinski hilbert space. Dragon new spiritual art mind expanding subliminal experience flower power abstract designs psychodelic pictures and meditative images beautiful graphics dramatic wild fantastic contemporary visual dream explosions neue spirtuelle computer kunst bewußtseinserweiternde unterschwellige eindrücke abstrakte designs psychodelische und meditative bilder visuelle fantastische phantanstische explosionen schöne grafik fantasie phantasie traum Fractal formulae fraktal formel mathematics imaginary numbers. Chaos theory science images geometry of nature mandelbrot amygdala frac'cetera mazes of the mind computer generated art patterns graphdev computer graphics. 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Mutation reduction factor generations invert radius outside colour double mutation levels Variable tweak central. Fractal witchcraft algorithm hallucigenic Added Humberto Baptista's Epsilon Cross variation positive proximity value internal orbitdelay timer PI box popcorn and popcornjul Humberto Baptista Pickover's Latoocarfian Unity fractal type Chuck Ebbert's biomorph showorbit Fractint mandel julia mandelbrot,mandelbrot set,mandelbrot generator,mandelbrot recipe,mandelbrot equation,mandelbrot set lyrics,mandelbrot competition,mandelbrot wiki,mandelbrot set generator,mandelbrot screensaver,mandelbrot zoom mandelbrod,mandelbrot,mandelbrot recipe,mandelbrod leland,mandelbrod nazi,mandelbrotmenge, fractint,fractint windows,fractint vista,fractint download,fractint xp,fractint for windows,fractint mac,fractint for mac,fractint osx,fractint tutorial, Rees Acheson (author of MANDELB), Damien Jones, Agner Fog, Terje Mathisen, Thomas Jentzsch, and Daniele Paccaloni. Bert Tyler Stone Soup story Logarithmic Palettes and Color Ranges Biomorph Colour Decomposition Finite Attractors Continuous Potential Distance Estimator parameters corner coordinates Leibniz greek geometers Brahe Copernicus Kepler Newton ellipse parabola, hyperbola planets comets and projectiles. Calculus differentiating derivative functions geometric tangent Weierstrass Cantor Peano Poincare Benoit Mandelbrot visualisation caltech escher mind pattern clifford pickover frac'cetera complex numbers and imaginary numbers ident iteration mathematics maths stunning mind-bogling and bizarre sound maze amazing drum-n-bass rhythm rythmus musik tanz selbstaehnlich selfsimilar In colloquial usage, a fractal is "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole".[1] The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured". A fractal as a geometric object generally has the following features: It has a fine structure at arbitrarily small scales. It is too irregular to be easily described in traditional Euclidean geometric language. It is self-similar (at least approximately or stochastically). It has a Hausdorff dimension which is greater than its topological dimension (although this requirement is not met by space-filling curves such as the Hilbert curve). It has a simple and recursive definition.[2] 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, and snow flakes. 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. The mathematics behind fractals began to take shape in the 17th century when philosopher Leibniz considered recursive self-similarity (although he made the mistake of thinking that only the straight line was self-similar in this sense). It took until 1872 before a function appeared whose graph would today be considered fractal, when Karl Weierstrass gave an example of a function with the non-intuitive property of being everywhere continuous but nowhere differentiable. In 1904, Helge von Koch, dissatisfied with Weierstrass's very abstract and analytic definition, gave a more geometric definition of a similar function, which is now called the Koch snowflake. In 1915, Waclaw Sierpinski constructed his triangle and, one year later, his carpet. Originally these geometric fractals were described as curves rather than the 2D shapes that they are known as in their modern constructions. The idea of self-similar curves was taken further by Paul Pierre Lévy, who, in his 1938 paper Plane or Space Curves and Surfaces Consisting of Parts Similar to the Whole, described a new fractal curve, the Lévy C curve. Georg Cantor also gave examples of subsets of the real line with unusual properties—these Cantor sets are also now recognized as fractals. Iterated functions in the complex plane were investigated in the late 19th and early 20th centuries by Henri Poincaré, Felix Klein, Pierre Fatou and Gaston Julia. However, without the aid of modern computer graphics, they lacked the means to visualize the beauty of many of the objects that they had discovered. In the 1960s, Benoît Mandelbrot started investigating self-similarity in papers such as How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension, which built on earlier work by Lewis Fry Richardson. Finally, in 1975 Mandelbrot coined the word "fractal" to denote an object whose Hausdorff-Besicovitch dimension is greater than its topological dimension. He illustrated this mathematical definition with striking computer-constructed visualizations. These images captured the popular imagination; many of them were based on recursion, leading to the popular meaning of the term "fractal". A relatively simple class of examples is given by the Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, and Koch curve. Additional examples of fractals include the Lyapunov fractal and the limit sets of Kleinian groups. Fractals can be deterministic (all the above) or stochastic (that is, non-deterministic). For example, the trajectories of the Brownian motion in the plane have a Hausdorff dimension of 2. Chaotic dynamical systems are sometimes associated with fractals. Objects in the phase space of a dynamical system can be fractals (see attractor). Objects in the parameter space for a family of systems may be fractal as well. An interesting example is the Mandelbrot set. This set contains whole discs, so it has a Hausdorff dimension equal to its topological dimension of 2—but what is truly surprising is that the boundary of the Mandelbrot set also has a Hausdorff dimension of 2 (while the topological dimension of 1), a result proved by Mitsuhiro Shishikura in 1991. A closely related fractal is the Julia set. Even simple smooth curves can exhibit the fractal property of self-similarity. For example the power-law curve (also known as a Pareto distribution) produces similar shapes at various magnifications. Three common techniques for generating fractals are: Escape-time fractals — These are defined by a recurrence relation at each point in a space (such as the complex plane). Examples of this type are the Mandelbrot set, Julia set, the Burning Ship fractal and the Lyapunov fractal. Iterated function systems — These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals. Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters. Fractals can also be classified according to their self-similarity. There are three types of self-similarity found in fractals: Exact self-similarity — This is the strongest type of self-similarity; the fractal appears identical at different scales. Fractals defined by iterated function systems often display exact self-similarity. Quasi-self-similarity — This is a loose form of self-similarity; the fractal appears approximately (but not exactly) identical at different scales. Quasi-self-similar fractals contain small copies of the entire fractal in distorted and degenerate forms. Fractals defined by recurrence relations are usually quasi-self-similar but not exactly self-similar. Statistical self-similarity — This is the weakest type of self-similarity; the fractal has numerical or statistical measures which are preserved across scales. Most reasonable definitions of "fractal" trivially imply some form of statistical self-similarity. (Fractal dimension itself is a numerical measure which is preserved across scales.) Random fractals are examples of fractals which are statistically self-similar, but neither exactly nor quasi-self-similar. Approximate fractals are easily found in nature. These objects display self-similar structure over an extended, but finite, scale range. Examples include clouds, snow flakes, crystals, mountain ranges, lightning, river networks, cauliflower or broccoli, and systems of blood vessels and pulmonary vessels. Trees and ferns are fractal in nature and can be modeled on a computer by using a recursive algorithm. This recursive nature is obvious in these examples — a branch from a tree or a frond from a fern is a miniature replica of the whole: not identical, but similar in nature. In 1999, certain self similar fractal shapes were shown to have a property of "frequency invariance" — the same electromagnetic properties no matter what the frequency — from Maxwell's equations (see fractal antenna). Fractal patterns have been found in the paintings of American artist Jackson Pollock. While Pollock's paintings appear to be composed of chaotic dripping and splattering, computer analysis has found fractal patterns in his work.[4] Fractals are also prevalent in African art and architecture. Circular houses appear in circles of circles, rectangular houses in rectangles of rectangles, and so on. Such scaling patterns can also be found in African textiles, sculpture, and even cornrow hairstyles. adornment, artwork, cartoon, decoration, depiction, design, engraving, etching, figure, frontispiece, halftone, image, line drawing, painting, photo, picture, plate, sketch, tailpiece, vignette art object artwork, composition, object of art, objet d'art, piece, study, art, artwork, oil, picture, piece, portrait, still life