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Author Topic: Real world Fractals  (Read 5689 times)
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Jules Ruis
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« on: October 08, 2006, 07:28:33 PM »

As you know, fractals describe geometrical objects that have more and more sub-structure as one views them at higher and higher magnifications. Fractals also approximately describe many real-world objects, such as clouds, mountains, turbulence, coastlines, roots and branches of trees and veins and lungs of animals.

Scientists and engineers and mathematicians and other people interested in these objects (such as a computer graphics person working to create an image of an artificial landscape) might use fractals in their work. For example, a biomedical engineer might want to calculate how much surface area covers the bronchial tubes within a human lung. Or maybe an environmentalist wants to estimate how many miles of coastline could be affected by a large oil spill. These are ways that scientists use fractals to describe or approximate the *structure* of a real (or imagined) object.
Another way scientists and mathematicians sometimes use fractals is in the field of nonlinear dynamics, where the behavior of a system is *described*  by a geometrical object in something called "phase space."  This object can assume many different forms, such as points or loops (circles, polygons, squashed ellipses, etc.). Points indicate the situation when there is no change in behavior, while loops describe when a system does the same thing over and over again continuously, (i.e. it "oscillates"). An example of another shape is a spiral. Dynamicists use the spiral to describe how a pendulum swings back and forth and gradually spirals into the origin as time goes on. 

As for fractals, there are some behaviors (often called "chaotic") that are so complex that the geometric object is a fractal, rather than a simpler shape. A cardiologist might monitor a patient's heartbeat and chart its behavior over time. A healthy patient might have a slightly irregular heartbeat,  and this might be visible in the record as a fractal. But if the heartbeat becomes too regular, the fractal might morph into a simpler shape, such as a loop, indicating that the patient might be at risk for a heart attack. In this example the fractal is used to help the physician monitor the status of her patient.

So you see that fractals can be used to describe the *structure* of things in the real world, or the *behavior* of systems in time.
« Last Edit: October 08, 2006, 07:30:36 PM by julesruis » Logged

Jules J.C.M. Ruis
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« Reply #1 on: November 13, 2006, 07:36:42 PM »

Jules - maybe I take >So you see that fractals can be used to describe the *structure* of things in the real world, or the *behavior* of systems in time ... a bit away / out of the context now ...

>*behavior* of systems in time, it was my impression here for photos I made last year at the danish Northsea Coast, Dunes nearby Skagen, at the top of Danmark. And, where I had really * Fractal Feeling * smiley
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Dunes , sand - impression for a very short while ...



***
A lot of Dunes are coined here from a natural  * Sandstorm desaster * in the 16. century , impression here ...


Margit
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Jules Ruis
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« Reply #2 on: November 13, 2006, 11:01:35 PM »

I think these two photos are excellent examples of fractals in nature, so of real world fractals.

Jules.
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Jules J.C.M. Ruis
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« Reply #3 on: November 14, 2006, 08:18:58 PM »

Jules wrote >I think these two photos are excellent examples of fractals in nature, so of real world fractals ...

Thank you Jules, here are 2 photos with same impressions from tide way ( Priel in german )
    http://i10.tinypic.com/435z8lv.jpg

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Margit
« Last Edit: October 01, 2013, 07:47:21 AM by Nahee_Enterprises » Logged
Jules Ruis
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« Reply #4 on: November 14, 2006, 11:18:02 PM »

How could Nature realise it ?!
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Jules J.C.M. Ruis
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« Reply #5 on: November 15, 2006, 03:32:04 PM »

I always love to see your wonderful photos, Margit!
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« Reply #6 on: November 15, 2006, 06:12:35 PM »

Jules wrote > >How could Nature realise it ?!

Thats a really good question Jules ...  but, I cannot answer :-)
For myself its the wonderful mystery of nature ...
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Tides ( Ebbe & Flut ) have as I think a great effect here ...

( http://en.wikipedia.org/wiki/Tide#searchInput )

Maybe thats a little point to start for a bit more explanation here  ? :-)))

Margit


PS::
Thanks for comments Titia smiley wink smiley
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kram1032
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« Reply #7 on: December 08, 2009, 03:31:56 AM »

The nature realises it by applying physics.
That's all the magic if you put it very simple.

The amazing part rather is that a lot of those formulae look quite short and simple. - usually the simpler ones give the more interesting results smiley

I'd love to see a super-complex ifs which combines for instance http://en.wikipedia.org/wiki/Lotka-Volterra_equation this with http://en.wikipedia.org/wiki/Bose_einstein_condensate that and other crazyness....
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oftakofta
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« Reply #8 on: December 19, 2009, 12:09:50 AM »

Jules wrote > >How could Nature realise it ?!

Thats a really good question Jules ...  but, I cannot answer :-)
For myself its the wonderful mystery of nature ...
***
Tides ( Ebbe & Flut ) have as I think a great effect here ...

( http://en.wikipedia.org/wiki/Tide#searchInput )

Maybe that's a little point to start for a bit more explanation here  ? :-)))

Margit


PS::
Thanks for comments Titia smiley wink smiley

As far as I understand it fractals in nature are the "scars" of chaotic (deterministic, but unpredictable) systems. To exemplify: The fractal nature of coast lines was investigated by Bernard Sapoval after he had been experimenting with fractal drums (which turn out to be extremely effective at damping waves). He concludes that "the reason why fractal coastlines exist is precisely because they are best at damping ... waves. As the coast damps down the waves, then the erosion to which it is subjected is reduced. They are thus stabilized by their fractal structure."


http://classes.yale.edu/fractals/panorama/ManuFractals/FractalDrums/FractalDrums.html Here is some more info and links to references.

One other example is the fractal nature of the human circulatory system with its ever-splitting tubes from the aorta down to the capillaries. The reason for this could simply be that fractals are great space-fillers so you get perfusion to the whole body. The genetic information that needs to be encoded (crudely) to achieve this marvellous feat of "engineering" is simply "IF tube THEN split it".

Finally a more concrete example on the interplay between fractals and deterministic chaos is the strange attractor observable in magnetic pendulums http://www.bugman123.com/Fractals/Fractals.html (thank you Bugman) Also a "real world" example can be fond at

<a href="http://www.youtube.com/v/Qe5Enm96MFQ&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Qe5Enm96MFQ&rel=1&fs=1&hd=1</a>


I have tons of clearly fractal images of bacteria, epithelial cells and bacterial in vitro infections from my microscopes (light & EM) that I plan to present here as soon as we publish the data.
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Dogamai
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« Reply #9 on: December 28, 2009, 01:11:16 PM »

I am wondering how many people have seen Nassim Harameins work...    theresonanceproject.org

It is now proven that the very structure of the space-time vacuum of our universe is in fact a true 3 dimensional fractal.

64 tetrahedrons. A 40 tetrahedron 3d "Star of David" plus 24 tetrahedrons in the form of an octohedron filling the gaps between the extreme vectors of the "Star", which also forms an octohedron inside, the sum of the most extended surface at any scale is a perfect sphere...   Hence: The sun, the earth, the moon, the galaxy, the Atom, the proton, the gluon, the higgs boson, the plankt black hole, etc etc...

SuperClusters of stars contain a "atomic structure" appearance, suns rotating at all angles around a center black hole / star

Now the question is, who is going to apply this to a virtual 3d platform (like video games of movies)...
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oftakofta
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« Reply #10 on: December 28, 2009, 01:42:22 PM »

I am wondering how many people have seen Nassim Harameins work...    theresonanceproject.org

It is now proven that the very structure of the space-time vacuum of our universe is in fact a true 3 dimensional fractal.

64 tetrahedrons. A 40 tetrahedron 3d "Star of David" plus 24 tetrahedrons in the form of an octohedron filling the gaps between the extreme vectors of the "Star", which also forms an octohedron inside, the sum of the most extended surface at any scale is a perfect sphere...   Hence: The sun, the earth, the moon, the galaxy, the Atom, the proton, the gluon, the higgs boson, the plankt black hole, etc etc...

SuperClusters of stars contain a "atomic structure" appearance, suns rotating at all angles around a center black hole / star

Now the question is, who is going to apply this to a virtual 3d platform (like video games of movies)...

I'm sorry but that makes absolutely no sense whatsoever. It sounds like pure numerology. If this person truly has a theory of everything it should be falsifiable. This means that it should make specific predictions about nature that independent investigators can confirm or deny through experiments.
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Nahee_Enterprises
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« Reply #11 on: December 30, 2009, 02:31:53 AM »

    I am wondering how many people have seen Nassim Harameins work...    theresonanceproject.org

A non-profit organization in Hawaii doing research.  Sounds more like a way to get others to donate money so that those at the organization will not have to find a real job doing real work, and they can then afford to live in a tropical paradise.    evil
 
« Last Edit: October 01, 2013, 07:52:29 AM by Nahee_Enterprises » Logged

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