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Post by Fusioner on Aug 3, 2005 4:15:24 GMT -5
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Post by Fusioner on Aug 3, 2005 6:38:10 GMT -5
dictionary.reference.com/search?q=fractal3 entries found for fractal  frac·tal 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 frctus, past participle of frangere, to break. See fraction.] fractal n : (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry Source: WordNet ® 2.0, © 2003 Princeton University fractal <mathematics, graphics> A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in). Many mathematical structures are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set and Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines. Benoit Mandelbrot, the discoverer of the Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break". He defines a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals. www.ultrafractal.com/Ultra Fractal is the best tool to create fractal artwork and fractal animations. Whether you are a graphics designer, a professional fractal artist, a video producer, or a complete beginner, Ultra Fractal 4 makes it easy to create beautiful fractal pictures, animated textures, and moving fractal backgrounds. Fractal Math had not been invented when Einstein was alive fusioner.proboards60.com/index.cgi?board=history&action=display&thread=1122978365Today with the processing power of a PC and a fractal software program... Very complicated and high resolution fractal graphics can be generated in short order... Software can model clouds, mountains, turbulence, and coastlines. This is a case where the math has caught up with, and imitates life... Which was the opposite approach taken by Einstein, where the math was created to address a specific problem. A universal theory that covers time and space... Electromagnetics and gravity... Will be derived as a result of fractal mathematics and studies.
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Post by Fusioner on Aug 3, 2005 6:40:15 GMT -5
 upload.wikimedia.org/wikipedia/commons/thumb/1/18/Mandelpart2.jpg/800px-Mandelpart2.jpg - Click for full size The Mandelbrot set, named after its discoverer, is a famous example of a fractal. en.wikipedia.org/wiki/FractalFractals of many kinds were originally studied as mathematical objects. Fractal geometry is the branch of mathematics which studies the properties and behaviour of fractals. It describes many situations which cannot be explained easily by classical geometry, and has often been applied in science, technology, and computer-generated art. The conceptual roots of fractals can be traced to attempts to measure the size of objects for which traditional definitions based on Euclidean geometry or calculus fail. |
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Post by Fusioner on Aug 3, 2005 6:46:57 GMT -5
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Post by Fusioner on Aug 3, 2005 19:37:32 GMT -5
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Post by Fusioner on Aug 4, 2005 5:11:44 GMT -5
 Rainbows are refraction patterns in nature... Light is fractal. |
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Post by Fusioner on Aug 4, 2005 5:17:41 GMT -5
 Iron powder on a bar magnet shows that electromagnetic lines of force are fractal in nature. |
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Post by Fusioner on Aug 4, 2005 5:20:53 GMT -5
 Lightning is Fractal |
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Post by Fusioner on Aug 4, 2005 5:29:48 GMT -5
 Snow Flakes are Fractal   So are branches on trees and bushes... |
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Post by Fusioner on Aug 4, 2005 5:43:09 GMT -5
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Post by indole on Aug 6, 2005 3:19:12 GMT -5
Howdy
explain how DNA is fractal?
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Post by Fusioner on Aug 6, 2005 10:45:47 GMT -5
There are no curves in nature... DNA consists of protein elements, they are ... particulates.... When bound together they form spirals... But the spirals are not curved... They are more like a spiral staircase... Angular elements forming a rotating structure... It's fractal not curved. Find me one true curve in nature  |
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Post by Devils advocate on Aug 6, 2005 20:02:16 GMT -5
Ok I'll bite the bait this time… Find me one true curve in nature On what scale? If a fractal is design conservation, then is it a legitimate claim that curves don't exist if you have to go to a molecular scale to prove that the curve is composed of subcomponent shapes? Consider the egg, on one scale it is visibly curved, if you must go to a molecular level to demonstrate that it is not curved then is there really design conservation? What about particle paths, such as the path of a comet or even a thrown projectile? Are these not curved? What about hail? Are they curved? What about cloud patterns viewed from space, they sure are fractacular but there are curves, at least on certain scales. If the curve is an imposed designation, an arbitrary demarcation of form, then curves don't exist outside of perceptive context regardless of nature. However if we are going to say that then we can say the same about fractals. Fractals are a means of demarcating design conservation, and thus exist contextually. Finding a fractal in nature is relative to perceptive context in the same way that finding a curve in nature is. One could easily claim that fractals don't exist in nature, and then use variable scale to demonstrate that what appears to be a fractal is composed of subunits or micro-units that are not conserved on a macro scale and vice versa. It is all dubious affair. It seems that knowledge is an illusion relative to context and really holds nothing. I wonder then though, to what end are you pursing the fractal? I too find awe in fractacular forms, and even that there is a conceptual aspect to it that explains how reality is an illusion of energy and even the elements being composed of the same subcomponents are part of but a single thing that exists. However to what end is this perception valid or relevant? Does it relate to our human vanity is supposing we have some sort of cosmic and consequential powers that make us so much more significant than a grain of sand or an ant? |
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Post by indole on Aug 7, 2005 1:26:24 GMT -5
There are no curves in nature... DNA consists of protein elements, they are ... particulates.... When bound together they form spirals... But the spirals are not curved... They are more like a spiral staircase... Angular elements forming a rotating structure... It's fractal not curved. Find me one true curve in nature 'Fractalness' is not based on curvedness or not-curvedness, but on self iteration. DNA does not consist of protein elements - DNA is not a protein, it's a nucleic acid. DNA strands are in some cases wound around protein molecules called Histones. But this has nothing to do with the DNA being fractal or not. Don't get me wrong, fractals are cool, and I'm not just trying to prove you wrong, but I'm interested to know if DNA really is a fractal. |
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Post by Fusioner on Aug 7, 2005 11:26:30 GMT -5
Watson and Crick discovered the geometry of DNA www.pbs.org/wgbh/aso/databank/entries/do53dn.htmlFranklin, working mostly alone, found that her x-ray diffractions showed that the "wet" form of DNA (in the higher humidity) had all the characteristics of a helix. www.time.com/time/time100/scientist/profile/watsoncrick.htmlAt a conference in Naples, Watson saw a vague, ghostly image of a DNA molecule rendered by X-ray crystallography.  Check out the photo. It has a crystaline structure. And to talk about curves... In large spaces, you can plot curves... It is a question of scale. But if you are going to Unify space, even large scale space... You have to unify regardless of your scale, the same physics has to apply on all scales, large and small in order to do that. You can't say that space, or energy, or electromagnetics, or even biology is curved sometimes and fractal at other times... They are fractal all the time, and on some scales they can be treated mathematically as curves... But it is an imprecise description, and if you change the scale, the notion of curves comes more into conflict with reality. It breaks down completely when you look at Einstein's curving of space on a large scale, compared to the fractal nature of quantum mechanics. Nobody has ever been able to resolve that conflict mathematically. There is no unified field theory either. |
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