what exactly is a fractal and is a pine cone an example?
958450
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.)
1049415
the universe is one big fractal and that is most likely true, but don't think to much about it or your head might explode. Our solar system is a tiny tiny aberration on the pinhead of space. There are parralels everywhere... in nature and in fractals. Think of it as so much bigger than your senses could ever understand and you'll be fine... just don't go killing busloads of people.
175375
Infinite is the correct answer. Just imagine a triangle. It has three sides. Add another and you have a rectangle. One more for a pentagon. keep going until you have an infinite number of sides and viola... a circle.
684006
I can't find much about bamboo's fractal aspects, if any. However the main form is a tube whose wall is strengthened by microtubes, so there is a degree of fractality, but it does not appear to go to lower levels. The structure is interesting as an example of natural optimization, though. Ref. 2 states that bamboo "has the ability to withstand high velocity winds. On a macroscopic scale the nodes, which occur periodically along the length of the bamboo, impart stability and rigidity to the plant. The cleavage and tensile strengths across the fibre direction are also raised considerably in the presence of the nodes. An analysis of the stresses experienced by the bamboo during bending indicates that the maximum stresses are generated at the outer part of the culm. The microstructure of the bamboo indicates that the density of distribution of the vascular bundles, which act as the reinforcing component, is the highest in the outer green layer." Ref. 3 contains some interesting detailed views of the bamboo microstructure.
868256
a circle has infinite lines of symmetry\n\nso does a straight line\n\nso does a sin wave\n\nthere are many figures that have infinit lines of symmetry\na more interesting question might be whether there are an infinite\nnumber of figures that have infinite lines of symmetry. (there are)
677194
I can arrange it in the form of a star such that at certain points and the sides of the star, there are trees there.\n\nNote: I think Kimon is repeating what I just said. I edited this just to note the fact that he repeated what I say, which is not deserving of a best answer.
1136350
Good Question, Mandelbrot's book and Barnsley's book will provide you with many examples.
169663
No, there is not. Circle is part of called Conic Graphs.\nA circle can be described as all points that are at the same distance (radius) of a fixed point (center). You can not give this kind of description about a triangle or square.\nNow, the truth is that you can describe -for example- an square with four lines (y=a , y=b, x=a, x=b)but you can not put everything in a single equation, besides this, this kind of lines are infinites (y=a from -inf to inf).\nThere are other kind of equations that gives you the area or perimeter of these shapes (i.e: b*h/2), but this is not what you're looking for.\nSo, again: There are NO equation of a triangle.
240497
Here is some information about tiling regular polygons (tiling is also called tessellation):\nhttp://mathforum.org/sum95/suzanne/whattess.html
599976
There are any number of examples. \n\nFor example many plant species and even entire communities have distributions controlled by soil type to the degree that it is normal to refer to sandstone communities or basalt communities.
750624
Try using the trial version of this software.\n\nhttp://www.ultrafractal.com/\n\nRegards, Zverb
771697
Try Google or Yahoo.  You'll find worked examples there.  I think it needs diagrams to understand; they and the accompanying explanations are too complex to attempt to reproduce here.
1176116
Its usually known as a frustum . Think of it as an upturned Bucket , essentially , top part of the a  cone cut off by a plane perpendicular to the axis .
910564
umm none that im aware of, what kind of mathamatics leval are you looking at?
108981
It is traditionally said that there are an infinite number of polymorphs for snow flakes.  They are all radially symmetrical and hexagonal though.
401893
First, topology is 'rubber sheet geometry' where things like angles and distances aren't important, but the number of holes is (since you can change angles and distances by stretching the rubber, but you can't change whether there is a hole.\n\nCombinatorics is the mathematics of counting things.\n\nAn example of combinatorial topology is given by Euler's equation. If you imagine paving a sphere with countries, and count the number of countries (F, for faces), the number of boundaries (E, for edges) and the number of places where three or more countries come together (V, for vertices), then it will always happen that F+V=E+2.\n\nIf, instead, you do this with a donut shape (a torus), you will find that F+V=E. In fact, each different surface has a slightly different formula that will hold no matter how it is paved with countries. This is a first example in combinatorial topology. You count various things (like countries) and find something that doesn't depend on specific paving, but rather on the type of surface it is.
691646
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.