Brains are fractals and could be mesured by fractal dimension

[Alef]

Google search for head fractal revealed links to some medical articles about brain matter degeneration, and using fractal dimension as way to mesure neural health. Long boring, but serious scientific article.
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2655112/



Quantifying degeneration of white matter in normal aging using fractal dimension.
http://www.neurobiologyofaging.org/article/S0197-4580(06)00227-2/abstract

Alsou there are article, saying that not only neurons look like fractals, but brains are organised like fractals
http://www.psychologytoday.com/blog/the-chaotic-life/200909/fractal-brains-fractal-thoughts
In that article are link to actual research with formulas, so maybe some guys would create new fractals around them;)

[Power 8]

Interesting! I suspected something of that nature when I rendered this image:



Unfortunately it was one of my early fractal renders and foolishly I did not save the parameters to that file.

Here are some other articles I read at the time:

 http://epub.ub.uni-muenchen.de/1675/
"the human cerebral cortex is self similar in a statistical sense, a property which is usually referred to as being a fractal. The presented analysis includes all spatial scales from the brain size to the ultimate image resolution. Results obtained in two healthy volunteers show that the self similarity does take place down to the spatial scale of 2.5 mm. The obtained fractal dimensions read D=2.73±.05 and D=2.67±.05 correspondingly...."

also
http://www.psychologytoday.com/blog/the-chaotic-life/200909/fractal-brains-fractal-thoughts

[cKleinhuis]

fractal dimension is used in many many fields of medicine, perhaps someoine could start making a list, as far as i know it is mentioned in the "CHAOS" book of james gleick, for steering a heart-pacemaker, it send a electronic pulse when the fractal dimension of the heart beat bumps is going close to a "euclidean" dimension ....

[kram1032]

Well, that list would consist of pretty much every single organ.
Even multiple times.
It's usually a matter of having a lot of functional area in a very limited volume, for instance in the brain, bowel or fingerprints.
The other thing, fractality is used in the body, is to efficiently spread materials or information across it, e.g. nerves or blood vessels.
Then, I guess, wrinkles in eyelids allow or effective rollup of them to a very narow space. I'm not sure but I'd guess that those wrinkles have a fractal pattern aswell.
Same goes for any wrinkles on the skin, eventhough most of them aren't directly an effect of function but rather one of... malfunction isn't the right word here...

Every single cell is a fractal on its own and so is the distribution of cells of certain functions.

Evolution is a fractal, obviously.
Humanity is a fractal.
Culture is a fractal.

Any bioelectrophysiopsychosociochemical thing our body does is a fractal. Aswell as each of the subterms that could be created from that.
That includes all the functions of the organs.

If you don't happen to look into something at the very last iteration of fractality - that always could happen in a physical world as you can't do infinite iteration depth - you'll probably find at LEAST one kind of fractal process in it.

[Alef]

The most important, this looks as pretty practical use. Render indeed looks very much alike of brains, especialy for first seconds.

[DonTen]

Ladies and gentlemen, todays word is: bioelectrophysiopsychosociochemical.
See how many times you can drop this into a conversation

[Chillheimer]

sorry to bump this old thread, but it turned up during my research for fractals&brains.
and there has been a very recent development that fits in here well, especially the first linked pdf about stroke damage in brains.
http://www.telegraph.co.uk/science/2016/06/03/stroke-survivors-walk-again-after-stanford-injects-stem-cells-in/
they injected stem cells directly into the damaged brain area, resulting in regeneration and in some cases people could walk again - even years after a stroke (previously any regeneration after 6 months was considered impossible)

[Max Sinister]

Since you bumped the thread: I'm not sure in which way brains are fractal. The 2d surface of them, sure, that's the only way to make the surface that big. (Any other reasons?)

But Neurons? I'm not sure... fractals are self-similar, but one neuron and many neurons seem to be very different, more so than a tree and a twig, or a mountain and a stone. Or, in another way: If you put many neurons together, you don't get something like a bigger neuron, but something different.

[Chillheimer]

sorry iif that's a bit lazy, but: http://fractalogy.org/brain/
also, the branching of neurons

[Max Sinister]

Thanks for the links. Here are my two cents:

On the Fractal Design in Human Brain and Nervous Tissue:
At the moment, I'm still wondering what a fractal dimension "between 1.1 and 1.5" means for a neural network. Obviously it's not about the brain's surface. But it has to be different than the Koch curve and the coast of Britain as well... more like an L-system of a tree? Also, the neural network is embedded in a three-dimensional space. Shouldn't that allow a higher dimension?

(Also, it's surprising that iterating with three copies of half the size isn't the same as six copies of one quarter the size. So much about 3/2 = 6/4.)


A Hierarchy of Time-Scales and the Brain:
Makes sense that since there are short and long events in the real world, our brain has to reflect both of them. Animals live mostly if not completely in the present...

But shouldn't there be more than just two time scales?

Also: Most artificial NNs (all I know of) usually process time the same way on all levels!


Modular and hierarchically modular organization of brain networks:

Small-worldness, indeed. And has to be modular too. Trying to understand modularity.

A hierarchical modular system... yes, that's fractal. "locally segregated processing".

"optimality at performing tasks in a changing environment" - that's certainly a good thing.


The Fractal Nature of the Brain:
"EEG Data Suggests That the Brain Functions as a “Quantum Computer” in 5‐8 Dimensions"

This is what I am very sceptical about. How did they measure this? The paper says nothing, only the sources, but I can't access them.