what exactly is a fractal and is a pine cone an example?

Question

I have a project in which I need to find a fractal in nature (i just happen to have pine cones) and was wondering if that was considered a fractal and how I might be able to analyze it by diagramming or whatever. what is something NEW related to architecture or interior design that could be made from the parts of the pine cone? (You dont have to answer it all, it would just be awesome if I had ideas! ) thanks in advance!

if it is not a fractal, can you please suggest an easy alternative that i could use as a fractal?

Answer 1

clouds
sea coastlines
river's outline
surface of the moon (& all the craters)
the surface of a brain
the bronchia of the lungs (pulmonary membrane on branching scales)
vascular system of the body or plant
certain trees/plants' limb structures.
are all examples of natural fractal objects.

As 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)

A leaf and all its veins might be a good one. You must have leaves. Fractal generated leaves:
http://mudandmuck.com/str2/FractalLeaves.jpg
The 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.

Just 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.)

Answer 2

A fractal is a repeating curve, no matter how large and how small; that is, an element of one aspect will, upon deep examination, look like the larger. The best easy example is a seacoast: the closer you look the more it becomes like the larger version viewed from far away. Ferns are the perfect example and there are easy computer programs that will make great looking ferns; look under fractal ferns in any search engine. A pine cone does not recapitulate the geometry. So, look to the fern Grasshopper

Answer 3

A fractal is an object of non-integer dimension, such as a complex recursive line that seems to fill space, therefore havng a dimension between 1 and 2. An important property of one class of fractals is that they are self-similar, so that regardless of what scale it's viewed, it looks at least about the same. For this reason, a pine cone is not an example of a fractal, since viewing it at smaller, microscopic scales, it does not look like a pine cone, for example.