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Author Topic: Isn't all nature fractal?  (Read 2403 times)
Description: Help with the basics for an essay.
0 Members and 1 Guest are viewing this topic.
charliemarie
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« on: October 07, 2009, 10:30:13 PM »

Hi there, I am having a bit of trouble with an essay I am trying to write and wondered if there was any help available? I have decided to study fractals in nature for my photography degree, and I am just getting my head around the basics, but I am a little confused;

After reading that fractals determine the shapes of nature, doesn't that mean everything that is nature, is fractal? But not all natural things are self similar...so how do you tell? For instance, I've researched a tree can be fractal, does this mean certain types of trees, or if you come upon a tree at a certain time of year, or all trees? Any help would be appreciated, because I am having trouble getting my head around this!

Thank you!

Charlie
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cKleinhuis
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« Reply #1 on: October 08, 2009, 11:30:09 AM »

hi there

self similarity is not the main point when talking about fractals in nature, self similarity is a way to easily create those objects

but i think every object is fractal which gets longer boundaries when changing the scale of the measure ... e.g. centimeters to milimeters, each time you get a significant difference in the lengthes, you can calculate a fractal dimension for that object ... and then you have a fractal, simply it is not representable with classical mathematical approaches... self similarity is just a nice side effect ...

 afro afro

you can browse this board ( fractals in nature ) to find interesting examples of fractals in nature
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lkmitch
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« Reply #2 on: October 08, 2009, 05:56:05 PM »

Rather than focusing (photography pun!) on self-similarity, I think the fundamental notion of fractals is roughness.  This can be mathematically expressed in terms of the increasing length (or area or volume) with decreasing scales, but informally, is the object rough?  In this view, trees, mountains, and clouds are generally seen to be fractal.  However, not all natural objects are fractal.  For example, consider a rock worn smooth by sitting at the bottom of a rushing river.  Or, the shell of an egg.  Or, a raindrop as it falls.  In cases of erosion, maximum strength, or minimum surface area, smoothness will often win and the object will not be a fractal.
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David Makin
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« Reply #3 on: October 09, 2009, 04:22:10 PM »

Personally I have a looser view of what constitutes being "fractal" - I tend to also include just about anything that is non-differentiable at any point and generally even for smooth rocks this will be the case (since the process of smoothing was almost certainly iterative) - plus of course even apparently "smooth" rocks are not smooth when magnified smiley
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cKleinhuis
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« Reply #4 on: October 09, 2009, 05:47:36 PM »

this opens an interesting point:

when the first iterations of measurement scale do not result in changing of size of the borders, when do the length starts to increase, and has this anything to say ?!?
 angel
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gamma
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« Reply #5 on: October 09, 2009, 07:31:16 PM »

Well, there are many systems that do not generate fractals, and randomness is ruining everything that dynamical systems generate. Fractals are something universal, a universality. Nature is a fractal... fractal that we know, over and over again.
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lkmitch
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« Reply #6 on: October 09, 2009, 07:59:15 PM »

this opens an interesting point:

when the first iterations of measurement scale do not result in changing of size of the borders, when do the length starts to increase, and has this anything to say ?!?
 angel

In my experience, this is a property of the particular object and way in which is it measured.  When I've seen the fractal dimension estimated using length/scale (i.e., the box-counting dimension), it's generally the measurements in the middle of the scale that "behave" the best and are used in the estimate.  So, the first few iterations may not be a good indicator of the "fractalness" of the object.
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charliemarie
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« Reply #7 on: October 10, 2009, 11:19:05 AM »

Thank you very much for all your help, it has cleared a few things up. I do however have another question!

I am writing an essay on how fractals have affected the way we live. Simple things like crowds, to family growth, to neighborhoods becoming towns etc and how this relates to chaos and fractals.  It is quite philosophical and I need to do a bit more research so I wondered if anyone knew of a good read about these topics? I'm unsure if I have enough material and debatable opinions to give my essay substance!

Thanks again

Charlie
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Cyclops
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« Reply #8 on: November 28, 2009, 10:22:15 PM »

I think true fractals can only occur in the virtual word because they have infinite scales. You can zoom and zoom on a fractal for ever, but no matter how 'fractal' and object appears there comes a point where it stops being 'fractal'
But yea there are many objects in the world about us that appear fractalicious, but not everything. Chaos on the  other hand is more universal! It defines almost everything and stops objects like trees being too fractalicious.
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Sensitively dependant on initial conditions
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