Print Page - Fractals & Nature

Here are a few images that illustrate this:
Some I made and some found on this forum
Animal:
(http://lariphotos.free.fr/fractales/mandelface.jpg)
(http://lariphotos.free.fr/fractales/hybridred2.jpg)
(http://lariphotos.free.fr/fractales/exthing2.jpg)
by mjk1093:
(http://i.imgur.com/4z2ys.jpg)

Vegetal:
(http://lariphotos.free.fr/fractales/flowerbulb.jpg)
(http://lariphotos.free.fr/fractales/mandelchou003.jpg)

by msltoe:
(http://www.fractalforums.com/gallery/1/803_23_03_10_7_03_01.jpeg)

Mineral:
(http://lariphotos.free.fr/fractales/marsrock1.jpg)

Vegetal & Mineral!:by Tglad:
(http://www.fractalforums.com/gallery/1/853_01_04_10_12_36_31.jpeg)

Quote from: Power 8 on April 05, 2010, 11:09:04 AM

I am often surprised at how often a fractal image will look like something out of nature. Vegetal, mineral or animal shapes frequently come to mind. This is even more true with 3D fractals like mandelbulbs and such. Does any one have thoughts, ideas or theories about this?

Well, we do have an entire section devoted to the concept - so there must be something to it!

http://www.fractalforums.com/fractals-in-nature/

Quote from: Power 8 on April 05, 2010, 11:09:04 AM

I kind of don't like this line of thought for two reasons. One is that the human brain is a pattern matching machine. Our brains, automatically will try to match shapes to known things, no matter similar, or dissimilar things are. For example, our brains process a colon, dash, closing parenthesis as a smiley face :-) If you really think about it, ) and : are so simplistic they don't resemble a face in the slightest. Our brain just insists on matching patterns. It's probably an evolutionary device that suited us well in the tens of thousands of years that we were here before civilization. Now it just makes typing more fun :-) :-P (^_^;)

I guess the second reason I like to avoid deep contemplation of fractals is that fractals are essentially numeric models of chaotic systems. Many things in nature are chaotic systems, so naturally there are going to be a lot of parallels between the two. But that doesn't imply any deep connection between the two or underlying principles that connect things like our beloved Z=Z^2+C to the branches of a tree any more than Newton's equations cause (or are caused by) the orbits of planets and behavior of gravity.

I love fractals and think they are truly aesthetically and scientifically fascinating, but I don't think that they hold any more secrets than the mathematical equations that have helped us model (the key word is model, not be responsible for in some way) other things in the universe.

This is just my opinion on things. I mean no disrespect to your observations.

No disrespect taken Aluminumstudios, on the contrary thanks for your views, which are insightful and exactly the kind of thing I was expecting when I made this post. Still I remain fascinated by fractals and get a pleasant feeling every time one reminds me of a natural shape... Why that is I don't know... Of course the laws of gravity existed long before Newton, and Romanesco broccolis existed long before Mandelbrot but I find the whole idea that man can find equations and formulas that describe natural geometrical or physical phenomenons to be intellectually stimulating.

The opposite works for me too:
(http://scienceblogs.com/chaoticutopia/upload/2006/11/broccoli.jpg)
detail of Romanesco broccoli

Well, I believe very strongly in a connection between fractal patterns and those of the real world!

Aren't Lorenz Fractals just his equations (which happen to work reasonably well!) for describing the weather?

I am Part-Scientist and Part -Mystic-Crazy-Hippy-Artist-Bastard! I have no problem believing that DNA acts on an iterative mathematical equation, and Only an iterative mathematical equation, and that Fractals will turn up as the driving force behind the evolution of that equation.

But then again, I like to believe that Qetzacoatl is returning in 2012 to EAT this Universe and poop out a new one.

I have no Scientific Basis for this (or many!) of my beliefs... But I do enjoy believing them, and don't care if I'm wrong, so it's just what I believe.

AluminumStudios, please check out the work of Max Planck. There are several systems that are "universal" - that is, the same effects can be observed in all of them, even if the equations or the large scale effects are completely different. For instance, the Mandelbrot version of the Newton fractal produces the exact same shape as the regular Mandelbrot set, because the two are "locally similar". The Mandelbrot set uses the same equation that appears in population dynamics, dripping water, convection currents, etc... in fact, there are some observations of "complex temepratures" (Yang-Lee zeroes), leaving the Mandelbrot set quite close to the real world. :)

Quote from: Power 8 on April 06, 2010, 02:24:09 AM

Maybe we share more of the same viewpoint than I thought. I find it satisfying and elegant that mathematics can model irregular things. I just shy away from the idea that some people put forth that there is some kind of deep, almost mystical or unknown connection between fractals and the universe. I remember reading on some web site a while back that fractals can heal us because of the fractal patterns of body tissues or something like that. I don't believe in those such things at all. But I certainly do acknowledge the elegant mathematical relationships in the world. For example (one that I heard and was fascinated by), is that for electrons to have stable orbits around atomic nuclei they must have certain energy levels. The energy of photon's that electrons emit and absorb corresponds exactly to the energy electrons must shed or gain to be in a stable nuclear orbit.

To whatever extend fractals play a role, nature is awesome :-)

On the contrary! I find it extremely likely that there IS some sort of underlying connection, but it's more simple than you'd think. When you think about it, fractal geometry is an ideal design for life--instead of having to specify the entire structure of a tree in its genetic code, all that's needed is a rule for generating the tree, like an L-system. It's no mystery why various forms in nature bear such a close resemblance to the fractals we work with. It's just efficient.

Though I have to agree with aluminumstudios--the notion that the connection is somehow mystical or supernatural is pretty strange. Fractals are, at their most basic level, purely mathematical constructs, and therefore any connection they may have with the physical world must also be purely mathematical.

Incidentally, Timeroot: it's always strange when we encounter complex numbers in physical quantities. I'd heard of an application of imaginary numbers in electrical engineering, but never of these Yang-Lee zeroes. Interesting.

I guess my feeling why fractals are seen in nature is that the rules that drive them are very simple, even though the results can look complicated. Moreover, euclidean geometry like straight lines or circles are really just special cases of fractals. What is a straight line if it isn't a recursive structure made out of self-similar smaller lines? There are just more ways of generating geometry which is rough (fractal) than the few ways that turn out smooth (like a perfect circle). If the rules operate about the same at different scales and in different directions and at different locations then that roughness should be fractal roughness.

I don't think all of nature is fractal, but I do think fractal geometry is one step better at describing nature than euclidean geometry (cylinders, boxes etc) since it generalises it.

And just as some natural objects are surprisingly euclidean (like pearls), some objects seem to be surprisingly fractal (like oysters :) http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1977 (http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1977)).. but most things aren't well described by either in my opinion.

I agree. The human body, for example, shows both fractal and Euclidean characteristics--our circulatory system is distinctly fractal, the interior of our lungs even more so, but our overarching structure (arms, legs, et cetera) is decidedly Euclidean. And, of course, the analogy to fractals breaks down at a certain scale, because everything has nonzero size--a living thing is built up of cells, a cloud of water molecules, etc. But I'd say that some sort of hybridization between Euclidean and fractal geometry ought to be sufficient to describe everything.

Thanks to all for your thoughts and insights.
Euclidian + fractal geometry can describe a lot of things but I guess there's still more to discover concerning the geometry of nature. Since Euclid lived in 300BC and fractal geometry was discovered in the second half of the 20th century, (Mandelbrot's publications are from the 70s) I hope it takes us less than 23 centuries to find the next step which is possible now we have the internet to share and bounce back ideas to an extent that Euclid never dreamt of. (or maybe he did dream of such things, he was a pretty fly guy for his time.)
I also feel, though I'm no mathematician that the triplex algebra discovered here is a pretty interesting discovery...
Reading Tglad's post where he says

Quote

What is a straight line if it isn't a recursive structure made out of self-similar smaller lines?

makes me think maybe euclidian geometry is englobed by fractal geometry which itself might be part of something still to be discovered...
Tglad also says:

Quote

some natural objects are surprisingly euclidean (like pearls), some objects seem to be surprisingly fractal (like oysters

so for fun I made a fractal pearl using Mandelbulb3D's Real Power formula, and a pearl is a sphere which is just a power 1 mandelbulb ;)

(http://lariphotos.free.fr/fractales/pearl2.jpg)
power 1.2 / zmul 1 / R stop 1.02

Finally about reesej2's post where he says

Quote

a living thing is built up of cells, a cloud of water molecules,

, well living things such as ourselves are also made out of water molecules as a cell is mostly water and 75% of our body mass is water but that is a different subject altogether that I also find fascinating, (the physics and proprieties of water ) . Water shows "fractality" too as for instance in these Google Earth pictures of rivers that look like trees:

(http://lariphotos.free.fr/googleearth%20art/rivertree01.jpg)

(http://lariphotos.free.fr/googleearth%20art/earthforest04b.jpg)

...and trees are fractal shapes too and they're made mostly of water... are trees vertical rivers?
Hmm I think i should go to bed now...

Nice pictures and some interesting thoughts, but I don't think that we should get too hung up on what percentage of our bodies or other things are water. Carl Sagan (a man who I deeply respect), once said "It's not the molecules that go into things, but the way they are put together." :nerd:

I wonder how often fractal patterns creep into human affairs without people ever being aware of fractal geometry and the like. This is Wat Arun (Temple of the Dawn), in Bangkok. I shot this photo a year ago, interested in the pattern, and only now realized how fractal it looks. (I know this isn't nature, but I see it as another example of the omnipresence of fractal patterns)
(http://farm4.static.flickr.com/3589/3601523081_e4e8e6fc67_o.jpg)

Nice find, the hellraiser mandelbox, that artist must of had some kind of demonic precognitive vision! And your thai temple photo is also very "mandelboxian" aluminumstudios, but as much as I also respect Carl Sagan, I have to disagree with you concerning water, I think it's largely taken for granted and overlooked, that it's massive presence in all life that we know of is not fortuitous, and that it will be discovered to play a very crucial part in the "putting together" of lifeforms. I've always found it odd to hear it said that life is "carbon based" when carbon makes for about 20% of the human body whereas water makes for 60 to 70%... But that's my own personal "metaphysics" and I hold no grudge against people who do not share these views.
It's just to mention these interesting pictures of snowflakes made by a William Bentley in the 1920s :

(http://aquavox.free.fr/snowflake.jpg)

Plenty more here: http://snowflakebentley.com/snowflakes.htm (http://snowflakebentley.com/snowflakes.htm)
some kind of "fractality" there too...

Quote from: Power 8 on April 09, 2010, 06:50:06 PM

I've always found it odd to hear it said that life is "carbon based" when carbon makes for about 20% of the human body whereas water makes for 60 to 70%... But that's my own personal "metaphysics" and I hold no grudge against people who do not share these views.

I never thought that made sense either.

DNA is Carbon based, sure. But we can't EAT pure Carbon like we can pure Water!

I'm not a biologist, so I can't say for certain, but I would guess that the "carbon based' classification is based on the role of carbon in organic molecules and it's chemical abilities. I believe carbon is present and the key building block that holds all molecules of life on Earth together due to it's electron arrangement which allow it to bond with many other atoms in many ways. Water acts as more of a medium and catalyst. While there is a lot of water in life, it's the large molecules held together by carbon that really define life for scientists.

Well, I happen to be a Chemist with a few courses in Organic Chemistry behind me (but admittedly few Biology courses). I think it's more Carbon's ability to bond with itself, forming long chains and rings and such, that allow it to be called the "Base" of Life.

But like many things in Science - it just sounds wrong and feels counter-intuitive.

I understand the reasoning behind the use of the phrase - as I said, DNA is Carbon Based, but that does nothing to make me FEEL Better about it!

I don't have to like it to acknowledge it and understand it.

I just think Water would be a better choice Aesthetically.

Sockratease, yes I agree carbon is a building block but I somehow feel water to be the builder. I guess this post is leaving the fractal domain to enter biochemistry... But it's a subject that I find really interesting though. If your sprinkle carbon over a seed like say an acorn, full of oak DNA, nothing much will happen , but add water...
There are a million examples like that. Where did life begin? In what substance does a foetus develop? etc... A chemist friend of mine said I was rambling about this because water is an inert substance.. This I clearly do not understand as to me water is one of the least inert substances on earth and seems always to be changing and moving.
I've been reading up on waterclusters on this interesting site by an english professor in chemistry:
http://www1.lsbu.ac.uk/water/index2.html (http://www1.lsbu.ac.uk/water/index2.html) It's quite fascinating...

But now back to fractals, bulbs and boxes, I made a new little mandelbulb video today using both Visions of Chaos and Mandelbulb3D:
http://www.youtube.com/watch?v=3LffNMiSkHc (http://www.youtube.com/watch?v=3LffNMiSkHc)

BTW Sockratease how's that fractal zoom for the independent movie coming?

Theses are pretty incredible too
Not Juliabulbs or Mandelbulbs but Pollen Bulbs rendered by Nature V1.0
http://www.swissinfo.ch/eng/multimedia/picture_gallery/Love_is_in_the_air.html?cid=8670836 (http://www.swissinfo.ch/eng/multimedia/picture_gallery/Love_is_in_the_air.html?cid=8670836)
(http://www.swissinfo.ch/media/cms/images/null/2010/04/011_armeria_400px-8668878.jpg)
(http://www.swissinfo.ch/media/cms/images/null/2010/04/060_tragopogon_400px-8669020.jpg)

just love philosophy. I have noticed patterns in almost everything. As I research more about Buddhism and reincarnation. Logically I could see how reincarnation could be considered an iteration. Karma, have that cause and effect property, maintains the pattern from one life to the next. All of this I see in a macro lens of the Universe. But the more I compare what fractals are against what is known in the universe I can project out logically and make a good guess that is more certain than just a leap of faith. Am I making sense?

I have many examples, but on lunch at work and want more time to write about it

Nature has always been fractal. We just needed to discover fractal geometry to duplicate it.

Quote from: Tim on July 24, 2010, 01:01:28 AM

Yes your making sense to me. I also love exploring differing philosophies. (as you can tell by my user name) :dink:

I found something from Przemyslaw Prusinkiewicz in his book The Algorithmic Beauty of Plants interesting to the discussion;

Quote

An interesting question, however, concerns the relationship between
fractals and real biological structures.

The latter consist of a finite number of cells, thus are not fractals in
the strict sense of the word.

To consider real plants as approximations of "perfect" fractal structures would be
acceptable only if we assumed Plato's view of the supremacy of ideas
over their mundane realization. A viable approach is the opposite one,
to consider fractals as abstract descriptions of the real structures. At
first sight, this concept may seem strange. What can be gained by
reducing an irregular contour of a compound leaf to an even more ir-
regular fractal? ...

By the way the emphasis in the quote is mine.

It's an interesting idea indeed. Are there true fractals in nature (in the strict sense of the word). That is objects that have infinite self similarity?

I tend to think that there must be and the scientists at the particle colliders will not find that last "building block" or fundamental particle system. With infinite time subdivision probably has no limit.

Iteron asks :

Quote

Are there true fractals in nature (in the strict sense of the word). That is objects that have infinite self similarity?

I don't think infinite self similarity exists in Nature but the romanesco broccoli, well known by Fractal forum members, is impressively fractal... Self similarity is not infinite but you can "zoom in" at least three or 4 times and find the same structure. It would be interesting to take macro or microscopic photos of it to see how far this goes...

(http://img.uphaa.com/uploads/347/romanesco-cauliflower.jpg)
(http://i12.tinypic.com/2n6hu6a.jpg)

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Real World Examples & Fractical Applications => Philosophy => Topic started by: Power 8 on April 05, 2010, 11:09:04 AM