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Mandelbrot Fractal Math??DMT's visual basis??

Migrated topic.
Regarding the relationship between mathematical systems, number theory and consciousness: Kurt Godel is the one who blows me away. And I like the way that Doug Hofstader brings his abstract concepts down to a grass-roots level in his latest book, "I Am A Strange Loop." I have paraphrased some of his ideas here.

Kurt Gödel was born in 1906 in Brunn, then part of the Austro-Hungarian Empire and now part of the Czech Republic. By 25 he had produced what many consider the most important result of 20th century mathematics: his famous "incompleteness theorem."
He pointed out that no system can perfectly describe and contain all possible elements of itself. Resulting in mathematical statements equal to "I am not a theorem."
Twists were Godel's specialty — twists in the fabric of space-time, twists in reasoning, twists of all sorts. And he postulates that the very basis of our sense of otherness and separateness(the I, or Self) is due to the fact that consciousness behaves like this loopy aspect of number theory.
Our sense of being as individuals, Self and "self" perception are consequences of the "I" looking back at itself and this can be described mathematically in all the implied beauty and limitations of any language.

Math is a human system of symbols (a language) with many short cuts, and I can thus describe "INFINITY" and still fit the description on this page! Language plays as huge a role as do our perceptions in establishing the body as a locus of identity.
We as Humans use and have symbols almost by definition!- which means my "I"and yours can exchange knowledge over great distances and time but we should be very careful not to confuse that symbol manipulation with who we really ARE, our Self.
Entheogens nudge our experience of this individual self to the side, in favor of the UberSelf? Perhaps oversimplified but that's my take on it this morning at least...
 
polytrip said:
Nice book about self referential structures: Gödel,Escher,Bach. by Douglas Höftsadter.
One thing that intruiges me about these fractal things, is that they contain a representation of infinity within a medium that is not infinite itself. Magical.
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:(

Hey Poly-

I missed this previous note of yours re: fractals and self-referential structure while reading through the thread earlier.
I loved GEB, and am reading a much newer book right now by Hofstader called, "I am a Strange Loop."
"I Am a Strange Loop" uses illustrations and some pictures, and certainly plenty of stories within stories (like GEB)but it is a little easier to follow the math, in my opinion, than in GEB. (This comment comes from the brain of someone who was studying Calculus 30 years ago but can't seem to balance a checkbook...ah memory)
I highly recommend to all psychonauts!
So much fun to see the impact mathmeticians have had on de-bunking mechanistic attitudes about the nature of consciousness.

Here's one that has a lot of great related stuff, posted by another Nexus member(I forgot who, just kept the link)
I am re-posting the link for the film series"Dimensions." There are many films here, the 4th one is on Mandelbrot and Julia numbers but the whole series is fun, with great visuals too:
Check them out!
 
benzyme said:
more like julia sets
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More fun with fractals, anyone? Whoever started this thread, thanks I think. It's an addictive topic] There are so many good gems out there in the public domain. They seem to be multiplying and proliferating like...spiraling seeds of galactic, um...whatever.

Sometimes a good laugh is just a <grin>
& this video is not so visually hypnotic but gave me a serious case of the giggles :d :lol: :!:


It's a music video about Mandelbrot's life from cradle to grave including the part about *discovery* of the Julia sets. What I find even more interesting is that there are so many other video versions of the same song - but totally different productions.
 
Here's one that has a lot of great related stuff, posted by another Nexus member(I forgot who, just kept the link)
Click to expand...

Must have been me ;)
It's a great series rendered in POVRay by Jos Leys, the closest you can get to 4d/hyperspace without the spice (DMT is the real thing of course!)

There are some great deep zooms into the Mandelbrot set on youtube, current computers are powerful enough to render animations far more detailed than the physical universe! This is sub-sub-sub-quark level...

Also recommended: Jock Cooper's work

Fractal Animations

Fractal Animations
www.fractal-recursions.com
 
Fractals... Random Patterns some would say... A contradiction in itself... Something can be either random, or have a pattern, but not both as randomness is without pattern and patterns are without randomness... Some also say there is no such thing as random. That which we call random is simply a pattern so large that we cannot recognize the pattern... Much like the universe... There are patterns in everything... Could this be just another bit of evidence of "intelligent design"?... If in fact there really does exist "intelligent design" then I submit to you that the universe in it's entirety is intelligent and fractals are just one of the universes expressions of art, much like the trees, the grasses, the clouds, and everything else. Maybe we are just a small speck of one very large fractal.
 
Check out this article from New Scientist: "Galaxy Map Hints At Fractal Universe".


The Traveler said:
Neo Guado said:
Check this out , raygirvan.co.uk 😉
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Hate to say this but that was an hoax:

Udo of Aachen - Wikipedia

en.wikipedia.org en.wikipedia.org
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That reminds me of this 13th century painting which I came across a number of years ago, to me it looks like Jesus (I assume it's Jesus, could be wrong) studying the geometry of a fractal...?

jk.jpg

en.wikipedia.org

Bible moralisée - Wikipedia

en.wikipedia.org en.wikipedia.org
 
Fractals... Random Patterns some would say... A contradiction in itself... Something can be either random, or have a pattern, but not both as randomness is without pattern and patterns are without randomness... Some also say there is no such thing as random. That which we call random is simply a pattern so large that we cannot recognize the pattern... Much like the universe... There are patterns in everything... Could this be just another bit of evidence of "intelligent design"?... If in fact there really does exist "intelligent design" then I submit to you that the universe in it's entirety is intelligent and fractals are just one of the universes expressions of art, much like the trees, the grasses, the clouds, and everything else. Maybe we are just a small speck of one very large fractal.
Click to expand...

Actually it doesn't hint to an intelligent designer at all because from simple systems more complex systems can arise completely naturally. This has to do with self organization. It doesn't require any designer it just requires stuff and the laws of nature. Of course we can ask why the laws of nature are the way they are but that's another subject.

Fractals are not everywhere. Chaotic systems can display fractal behavior. Fractal behavior is a behavior of chaotic systems. Self similarity is a term for this kind of property of fractals.

Chaotic behavior can as systems get more complex. Its an emergent property of certain systems.

Anyway many things in nature have self similarity but not at all scales. Also many patterns in nature appear as fractals but are not true fractals at all scales. For example a fern. It looks like a fractal but when you get down to the cellular level it doesn't look like a fractal at all. Its not really a fractal. Everything is not fractals. That's why I think all this mandelbrot fractal math stuff is taken way too far. It sells books but it doesn't convince me of any superstitious spiritual notions.
 
Also if you take any equation and feed it back into itself, then plot the answers, you get a fractal.... it could be that fractals observed everywhere are just manifestations of infinite feedback... which isn't as complex as it first seems... like how a tree grows into branches, that's fractal bio feedback, the same rule feeds back into itself over and over again, seed, grow a branch, leaf, seed, grown a branch, leaf, seed, grow a branch, leaf, seed, grow a branch off that and so on.... infinity is implied in infinite feedback (maybe)... it's like that question, how long is a coastline?, the answer is that it depends on the size of your measuring stick, if it's a very long stick, you'll get a much smaller answer than if you use a short stick... a coastline is infinitely rough, fractals can be used to measure roughness.
 
I should add that the reason your brain sees so many fractals on psychedelic drugs like dmt could be that it gets stuck in some kind of feedback loop and creates recreating the same image back on itself over and over to make a fractal. so yes to the original question i do think your brain is capable of generating images of fractals when it gets stuck in some kind of signalling loop while under the influence.
 
In the Arthur C.Clark video (was a while ago I watched so if I'm talking about the wrong movie, slap me) they use fractal equations to build computer generated landscapes that look like mountains, trees etc.
Well our brain is like some kind of computer so we should have a "program" that deciphers all the information coming in trough our optical nerve (Imagine billions of photons hitting the lens of your eyes in mere seconds) and to rebuild it as something we can understand.
So maybe the fractals we see is the program/internal computations used by our brain to make sense of what we see.
 
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