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Author Topic: Are Radiolaria an Example of a Mandelbulb?  (Read 10090 times)
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Paul Miller
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« on: December 14, 2009, 05:43:55 AM »


Radiolaria

http://www.ucl.ac.uk/GeolSci/micropal/radiolaria.html

Radiolaria are holoplanktonic protozoa and form part of the zooplankton...


http://www.ucl.ac.uk/GeolSci/micropal/images/radi/radi035.gif



         Alievium superbum (Squinabol)             


http://www.ucl.ac.uk/GeolSci/micropal/images/radi/radi036.gif



            Detail
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cbuchner1
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« Reply #1 on: December 14, 2009, 11:52:49 AM »


Radiolaria are holoplanktonic protozoa and form part of the zooplankton...





Fractal zooplancton generated by a generalized mandelbulb approach. wink
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kram1032
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« Reply #2 on: December 14, 2009, 03:05:56 PM »

It's not too unlikely that those are "generated" by iterations over spheres, so probably the Mandelbulb with {r*a,\phi*b,\theta*c} will hold a lot of nice creatures smiley
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twinbee
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« Reply #3 on: December 16, 2009, 01:34:31 AM »

Impressive find.

Perhaps less so now, but the Julia variation looks like these too (still Radiolaria):

From http://katespeidel.files.wordpress.com:


From www.cushmanfoundation.org:
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Dranorter
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« Reply #4 on: December 29, 2009, 05:23:00 PM »

Those spikes look familiar; wasn't there some variation of the Mandelbulb which had them?
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cKleinhuis
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« Reply #5 on: December 29, 2009, 05:40:12 PM »

it is an option in subblues version, multiplicating the y component of the triplex after each iteration
http://www.fractalforums.com/mandelbulb-implementation/mandelbulb-ray-tracing-plugin-for-photoshop-aftereffects-and-quartzcomposer/
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ker2x
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« Reply #6 on: January 01, 2010, 04:16:31 AM »


A 3D MandelBar ?  grin
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often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
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hobold
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« Reply #7 on: February 05, 2010, 05:03:11 PM »

If I remember correctly, nature uses a "generating algorithm" for such patterns that is not aware of the global shape, but locally imbalances concentrations of some molecules. The fur patterns of, say, a leopard were an example of that. It's a little bit like a standing wave of defined frequency, confined to the finite surface of some arbitrarily shaped object.

Or in other words, those spherical radiolaria are covered in "grid cells" that have pretty much the same local geometry everywhere. But as there is no "pole", those grid cells do not define a globally consistent coordinate system. Which in turn means that nature doesn't really have fractal iterations available as a viable algorithm.

But the small structures certainly do look fractal, while the large spikes are placed very regularly. Nature uses what works, and doesn't care for conceptual elegance.
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Timeroot
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« Reply #8 on: February 06, 2010, 01:05:43 AM »

Hobold has a point, but I suppose one would need to know more about how they developed in order to have any support for that argument. Imagine it like this:
 Trees start growing with a trunk, then branches grew off the trunk. Once they are done growing, new ones start growing off these, etc. In this case it is true, because each new branch doesn't know where the base it is; it just knows it needs to be, say, 1/2  the size of the previous branch. If this is analogous to how Radiolaria develop, Hobold's argument makes sense.

 Now image that trees grow from a "Bonzai" form to their full form, without losing much shape, only scaling up. This is similar to how humans grow: at a certain stage, cells differentiate and a global structure and coordinate system develop. (Think pole=torso or pole=head.) In this case, the argument is invalid (mostly).

Finally, I would like to point out that many fractal algorithms do function like trees - think Lindenmeyer Systems. Each line segment doesn't know where it is, it just knows what to develop into. And when all the pieces fit together (think Dragon Curve, line segments=cells), you get something completely fractal, with the cells/lines impossible to distinguish.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
kram1032
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« Reply #9 on: February 06, 2010, 01:22:18 AM »

No offense hobold, but did you read through what you wrote yourself? smiley

This generating algorithm is based on randomness but a randomness following special rules.

One of them is, fill as much space as possible with a surface as small as possible, which is exactly the reason for the spherical shape.
It's not like the atoms/molecules would need to know that rule. It just happens to be more stable than a cubic shape.

Basically, there are repeated rules in the randomness itself, causing a fractal.
Just not as algebratic as the mandelbulb.
It's an algorithm, dependend a lot on brownean motion, thermodynamics, fluid dynamics and rule of the lowest energy.
Maybe at that scale, quantum effects still play a role too...

For a lot of our proteins to work as they work, they certainly rely on quantum mechanics as certain movements aren't possible otherwise...
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hobold
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« Reply #10 on: February 06, 2010, 07:25:49 PM »

It's an algorithm, dependend a lot on brownean motion, thermodynamics, fluid dynamics and rule of the lowest energy.
You are probably right that random (stochastic) fractal processes do not need to depend on any larger scale global rules like some consistent coordinate system.

But the fact remains that the overall shape of this microorganism is not self similar across all relevant scales. In other words, a three dimensional fourier transform of this thing would not obey the fractal rule of 1/f^b. That's why I mentioned this other mechanism that I can neither name nor explain in more detail. The only thing I still remember about it is that I thought "so this is nature's way of doing Perlin noise!" (which is an algorithm used in computer graphics to generate narrow band noise of defined frequency).
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kram1032
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« Reply #11 on: February 07, 2010, 12:03:04 AM »

Well, no matter which realworld object, to allow it to be a fractal, you'll need to slightly loose the restriction of repeating on all scales.
Natural things just can't grow infinitely small, nor can they grow infinitely large...
Also, you could call the whole group of radiolaria a fractal, rather than a single one.
They're all quasi-self-similar to each other smiley

"All radiolaria are made equal, but some are more equal than others  evil"
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Timeroot
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« Reply #12 on: February 07, 2010, 12:34:11 AM »

"All radiolaria are made equal, but some are more equal than others  evil"
Is that a quote from Zooplankton Farm?
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
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« Reply #13 on: February 07, 2010, 10:11:36 AM »

For years I have tried to replicate those beautiful shells..mostly using stochastic methods..in some ways, I have succeed with simple ones..

Some examples are in my website: http://www.rfractals.net/gallery/main.php/v/Radiolaria/

They aren't related to the mandelbulb, but the way that they work gives me a little insight of how real radiolarians are created.




* FractalRadiolaria.jpg (187.76 KB, 700x700 - viewed 894 times.)
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« Reply #14 on: April 07, 2011, 07:37:53 PM »

For years I have tried to replicate those beautiful shells..mostly using stochastic methods..in some ways, I have succeed with simple ones..

Some examples are in my website: http://www.rfractals.net/gallery/main.php/v/Radiolaria/

They aren't related to the mandelbulb, but the way that they work gives me a little insight of how real radiolarians are created.




I visited your page. Really interesting. How did you create those structures? (I'm a newbie in this 3d fractals procedures).
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