any facts, info. or anything about fractals?
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A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales. The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales. A plot of the quantity on a log-log graph versus scale then gives a straight line, whose slope is said to be the fractal dimension. The prototypical example for a fractal is the length of a coastline measured with different length rulers. The shorter the ruler, the longer the length measured, a paradox known as the coastline paradox. \n\nThe term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable. \n\n"The" Mandelbrot set is the set obtained from the quadratic recurrence equation \n\nZn+1 = (Zn)^2 + C\n\nWhere Z0 = C in the complex plane for all C which this recurrence does not tend toward infinity.
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clouds\nsea coastlines \nriver's outline \nsurface of the moon (& all the craters)\nthe surface of a brain\nthe bronchia of the lungs (pulmonary membrane on branching scales)\nvascular system of the body or plant\ncertain trees/plants' limb structures.\nare all examples of natural fractal objects.\n\nAs far as i can determine pine cones don't have scaling similarity and thus are not good candidates for a fractal project.  (scaling similarity is not necessary for a fractal but it helps for display purposes!  there are many nonscaling and also random fractal sets.  The Apollonian gasket in the former and certain random walks in the latter.  Many people are under this misapprehension)\n\nA leaf and all its veins might be a good one.  You must have leaves. Fractal generated leaves:\nhttp://mudandmuck.com/str2/FractalLeaves.jpg\nThe smaller you look at a fractal, the more you notice that the very little parts look very similar to the big part(s).  That is one of the characteristics of a self-similar fractal.\n\nJust for edification.  While many fractals have a non-integral dimension, not all of them do (as has been claimed elsewhere). The definition of a fractal is a set for which the Hausdorff Besicovitch dimension strictly exceeds its topological dimension. (This probably does not help you much if at all.  It needed to be said however as others have misinterpreted what exactly a fractal is.)
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try this site has some interesting information:
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http://chemlab.pc.maricopa.edu/PERIODIC/periodic.html\n\nHere you can click on an element and see facts on it.\n\nCa<Cr<W
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A common type of fractal dimension is the Hausdorff-Besicovich Dimension, but there are several different ways of computing fractal dimension.  \n\nRoughly, fractal dimension can be calculated by taking the limit of the quo-  \ntient of the log change in object size and the log change in measurement  \nscale, as the measurement scale approaches zero. The differences come in  \nwhat is exactly meant by "object size" and what is meant by "measurement scale" and how to get an average number out of many different parts of a  \ngeometrical object. Fractal dimensions quantify the static *geometry* of an object.  \n\nFor example, consider a straight line. Now blow up the line by a factor of two. The line is now twice as long as before. Log 2 / Log 2 = 1, corresponding to dimension 1. Consider a square. Now blow up the square by a factor of two. The square is now 4 times as large as before (i.e. 4 original squares can be placed on the original square). Log 4 / log 2 = 2, corresponding to dimension 2 for the square. Consider a snowflake curve formed by repeatedly replacing ___ with _/&#92;_, where each of the 4 new lines is 1/3 the length of the old line. Blowing up the snowflake curve by a factor of 3 results in a snowflake curve 4 times as large (one of the old snowflake curves can be placed on each of the 4 segments _/&#92;_).  \nLog 4 / log 3 = 1.261... Since the dimension 1.261 is larger than the  \ndimension 1 of the lines making up the curve, the snowflake curve is a fractal.
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Here's a nice site:\n\nhttp://www.mathematische-basteleien.de/tangrams.htm
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How are you even sure that such a function exists? the numbers look very random.
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There really doesn't seem to be much on the internet about them. Try the links below.
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Have you tried http://en.wikipedia.org/wiki/Main_Page they have info about anything.
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Ott, Edward (2002). Chaos in Dynamical Systems. Cambridge University Press New, York. ISBN 0521010845. \nGutzwiller, Martin (1990). Chaos in Classical and Quantum Mechanics. Springer-Verlag New York, LLC. ISBN 0387971734. \nMoon, Francis (1990). Chaotic and Fractal Dynamics. Springer-Verlag New York, LLC. ISBN 0471545716. \nTufillaro, Abbott, Reilly (1992). An experimental approach to nonlinear dynamics and chaos. Addison-Wesley New York. ISBN 0201554410. \nGollub, J. P.; Baker, G. L. (1996). Chaotic dynamics. Cambridge University Press. ISBN 0521476852. \nBaker, G. L. (1996). Chaos, Scattering and Statistical Mechanics. Cambridge University Press. ISBN 0521395119. \nAlligood, K. T. (1997). Chaos: an introduction to dynamical systems. Springer-Verlag New York, LLC. ISBN 0387946772. \nKiel, L. Douglas; Elliott, Euel W. (1997). Chaos Theory in the Social Sciences. Perseus Publishing. ISBN 0472084720. \nStrogatz, Steven (2000). Nonlinear Dynamics and Chaos. Perseus Publishing. ISBN 0738204536. \nSprott, Julien Clinton (2003). Chaos and Time-Series Analysis. Oxford University Press. ISBN 0198508409. \nHoover, William Graham (1999,2001). Time Reversibility, Computer Simulation, and Chaos. World Scientific. ISBN 981-02-4073-2. \n Beauty of Fractals, by H.-O. Peitgen and P.H. Richter \nChance and Chaos, by David Ruelle \nComputers, Pattern, Chaos, and Beauty, by Clifford A. Pickover \nFractals, by Hans Lauwerier \nFractals Everywhere, by Michael Barnsley \nOrder Out of Chaos, by Ilya Prigogine and Isabelle Stengers \nChaos and Life, by Richard J Bird \nDoes God Play Dice?, by Ian Stewart \nThe Science of Fractal Images, by Heinz-Otto Peitgen and Dietmar Saupe, Eds. \nExplaining Chaos, by Peter Smith \nChaos: Making a New Science, New York: Penguin, by James Gleick \nComplexity, by M. Mitchell Waldrop \nChaos, Fractals and Self-organisation, by Arvind Kumar \nChaotic Evolution and Strange Attractors, by David Ruelle \nSync: The emerging science of spontaneous order, by Steven Strogatz \nThe Essence of Chaos, by Edward Lorenz \nDeep Simplicity, by John Gribbin \nThe Road To Chaos, by Yoshisuke Ueda \nThe Chaos Avant-Garde: Memoirs of the Early Days of Chaos Theory, Edited by Ralph H. Abraham and Yoshisuke Ueda
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Details, details? what kind? how big? purpose?
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Try this one.\nhttp://chemlab.pc.maricopa.edu/periodic/stowetable.html
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It is named "magic square" and they are very well investigated.\nExapmple of it's history and other information is, for example, in the first attached wiki article.\n\nThere are 275,305,224 such 5x5 squares.\nMethods for building them can be found in a references of this wiki article.\nFor example, 2nd attached URL is a link to an application, which can generate you a lot of them.\n\nNow, some examples:\n\n01 02 17 23 22\n19 15 08 16 07\n20 14 13 12 06\n21 10 18 11 05\n04 24 09 03 25\n\n\n01 02 17 23 22\n20 16 08 15 06\n19 12 13 14 07\n21 11 18 10 05\n04 24 09 03 25\n\n\n01 02 17 23 22\n20 16 08 15 06\n21 12 13 14 05\n19 11 18 10 07\n04 24 09 03 25\n\n\n01 02 17 23 22\n21 15 08 16 05\n19 14 13 12 07\n20 10 18 11 06\n04 24 09 03 25\n\nand so on
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Expanding on the above response on the Pareto principle, you can also demonstrate fractals, e.g. if 80% of the sales come from 20% of the customers, 80% of the sales from those 20% will come from 20% of those 80% assuming a large enough set.  Confusing?  I love fractals and think your question is awesome.
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Yes!!!!!!!!! Email me, and I'll try to shed more light on this. Parabolas are where my genius comes out :)
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square-ish in shape\ncome in different sizes\nmany varieties
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You ask a number of questions here.  I will first say that the Mandelbrot set does not really have any direct practical value.\n\nThe mandelbrot set like other fractals is interesting, in that they are calculated out in iterations, and the number of iterations used determines whether or not a point is in the set.  To give an example, you know that if you define a function 2=x+y, you take any two values for x and y and see if they fit that function.  x=2, y=3 is not a point that fits this function, whicle x=0.5, y=1.5 does fit this function.\n\nWith the Mandelbrot set, you cannot look at a point and see if it fits the function.  The way the madelbrot set is formed is to place imaginary numbers on one axis, real numbers on the other, and define the points as follows:\n\nfor any complex number z, such that z=z^2 + 1, iterated over and over does not ever exceed 2, that number z is part of the set.\n\nThere is only one way to determine if a number z is part of the set and that is to say, we are going to do a certain number of iterations, and if z<2 at the end of our calculations, that z is part of the set, otherwise it is not.  This means that whether or not a complex number is part of the madelbrot set depends on the number of iterations you use in your inclusion criteria for z.  There is no absolute answer to the question "Is z a part of the madelbrot set?"\n\nSO yes the Mandelbrot set does go on forever, and the more iterations used in calculating it, the more detailed the fractal gets.