/sci/ - Science & Math

that is very difficult to say, as you have no objective way of measuring the complexity of the figures during a psychedelic experience.

On the other hand you could probably safely bet that we've been thre for a while. I don't know. In my case I was always able to pinpoint the steps I'd use in photoshop to recreate what I'm seeing

then again I am a graphic designer so it might be a special case

>>7032754
>How much processing power would be needed at minimum to render in real-time the sort of fractal geometry that is commonly observed while having a psychedelic experience?
Fucktons.

>Is it rational to evaluate the iterative capability of the brain as if it was a processor?
Not even remotely, the brain is a neural network that processes information through connections between neurons, the computer uses centralized logical processing with RAM, I don't really know how any of the technical bits work but your brain is a completely different kind of computer from a machine.

>Is it rational to evaluate the observed fractal geometry as if it was complex plane transformations?
Rational, perhaps, if one wishes to investigate it and has some means of doing so, but it's certainly not meaningful; or, if it is meaningful, finding that meaning requires such a huge gap of currently missing knowledge it is for all intents and purposes meaningless in the short-to-medium-term.

>Why does it look, at times, exactly like complex plane transformations?
It doesn't "look like" complex plane transformations, it looks like graphical representations of complex plane transformations. Maybe because there's something more to it, maybe because when your mind sees a ton of mathy shit with far too much detail to process it perceives similarity where there is none, maybe all the people writing visualization software for complex plane transformations have smoked too much DMT.

>The complex plane has its own distinct way of presenting fractal geometry so isn't the striking similarity surprising?
There's a lot about fractals that's pretty surprising.

If the processing power analogy isn't sound, then how about the frequency of recurrent excitation?

personally, having seen lattice networks under the influence of DMT, I just assume that's a visualization of some underlying geometry that's part of "normal" brain processing to generate visual representations of space.

basically, you're seeing behind the curtain, but it's all lit up

>>7032809
Extremely intricate fractals behind the scenes, 24/7? Lattice networks seem more logical for that.
Fractals are generally recursive phenomena and recurrent excitation is one of the main aspects of psychedelia, it's easier to see them as a product of the state.

>>7033608
Remember anon we draw landscapes on computers with 'fractals' to pretty good effect.

This is pretty much what DMT looks like for me btw but it sort of goes into overdrive

>>7032809
If you want to see some trippy shit stare down at a bed of pebbles maybe 2-3cm to 1mm in diameter

How characteristic are Julia sets to the complex plane? Could Julia sets be formed with identical visual results in other mediums than the complex plane?
Besides the definition of being the converging points of the iterative formula, what other methods could produce structures that are extremely similar in appearance to Julia sets?
I'm asking specifically about Julia sets because a certain dose range of LSD will inevitably give me very Julia-esque geometry, with the basins of attraction and other properties being nearly identical.

And why would any of this have meaning? Mostly because it's very interesting but to name an actual meaning, I'd say understanding how the brain iterates geometry tells a lot about how it functions. Even more so than analysis of what we normally perceive because the nature of the observed fractal geometry isn't strongly dependent on input - it's intrinsic to the brain. It can form out of a null background.

Dammit /sci/ you're making me want to do drugs

>>7033751
You assume introspection is worth anything in studying brain functions, which is dubious.

You have an ill understanding of the math you're talking about. What is a 'medium' and why is the complex plane one?

And, in response to the questions in OP, is it really that absurd that the human mind finds a similarity between one product of the human mind (complex plane, fractals) and another (visual hallucination)? No, it's not.

Furthermore, the computer-analogy for the human mind is not really that workable any more. For one, we came to realize a computer always comes with a computer-guy, a user, while this is not the case with the mind.

But great threat otherwise.

>>7033776
>What is a 'medium' and why is the complex plane one?
The complex plane is where the complex number operations for fractal structures are carried out and contains the fractal sets produced as a result of these operations. Medium seems like an appropriate word. Does this have an actual term? Would domain be more appropriate?
>similarity between one product of the human mind (complex plane, fractals) and another (visual hallucination)
How is it any more hallucination than anything we see?

>>7033800
>The complex plane is where the complex number operations for fractal structures are carried out and contains the fractal sets produced as a result of these operations.
what does that even mean.
>How is it any more hallucination than anything we see?
By lack of external stimulus

>>7033810
Are you serious?

Bump.

>>7033810
>By lack of external stimulus
This is a depiction of external stimulus acting as the seed for the generated fractal geometry.

>>7032754
>Is it rational to evaluate the iterative capability of the brain as if it was a processor?

Not really. The brain is asynchronous and doesn't really process things in "steps" at all, and does things in parallel instead of sequence anyway. Not to mention that any attempt to convert a neural network's "function" into any sensible series of mathematical operations is nonsensical at best.

What (I think) OP is trying to get at is that maybe the brain does something similar to a complex plane transformation during image processing. Then, when drugs happen, something fucks up and we get a few extra layers on top.

Sort of like how our ears do a Fourier transform on incoming sound waves. We break the wave down into its individual frequencies and send that to the brain.

>>7035388
What? I've programmed a neural network.
http://en.wikipedia.org/wiki/Artificial_neural_network

>>7035429
Yes, and you cannot easily convert what that neural network is doing to an algorithm. The network can, obviously, be implemented with simple math, but you cannot decompose the network itself into "And THIS collection of neurons implements an addition operation"

>>7035388
>>7035436
you sound like one of those autists who insist every phenomenon must be expressed in the most fundamental laws of physics known or else it's worthless pleb "soft science"

it's extremely useful to abstract underlying microcircuits into some effective theory and work on a higher level scale, and these things happen all the time. the brain suffers from division of labor like every other organ. how do you think translation between psychobehavioral and mean field / spiking neural network models happens?

>>7032754
I have exactly what you're looking for:

http://www.math.utah.edu/~bresslof/publications/01-3.pdf

>>7033846
why shouldn't I be?

>>7035520
Strongly related but the paper seems to be exclusively about form constants which I'd perceive as a phenomenon that differs fundamentally from fractal geometry. Though probably they share many principles as they're both forms of algorithmic geometry that are seemingly hardwired to appear in certain neural conditions.

>>7035426
>What (I think) OP is trying to get at is that maybe the brain does something similar to a complex plane transformation during image processing.
Absolutely. If the products of iterative processes of both systems appear extremely similar, how could there be no similarities in general?

Bump.

This type of "sharp" seemingly infinitely extending branching is something I have observed against the lighted background behind my eyelids. It differs from the depiction in the image in the way that the branching leaves a kind of geometrical "tension" in the surrounding background. It gives an appearance of depth, as if there was a height map associated to the fractal. Depending on intensity, these height maps can curve even further and into higher dimensional objects.
It is sometimes hard to determine "where" in the visual field the fractals are. For example, it can seem like they extend from the "behind" of the visual field, especially when the eyes are closed.
It is important to note that in sufficiently strong psychedelic states, the concept of dimensions is altered to such an extent that there is no longer a consistent image of "where" the observer is in terms of the geometry. This essentially means that while in this state, the observer can perceive itself as the geometry, either universally or partially. Thus, while this is happening, it is not a matter of understanding the geometry as an external entity but rather, being it.
Especially in stronger psychedelic states, there can also be a temporal element associated to the geometry. When perceiving oneself as a sub-region belonging to some further extending geometric construct, it can be apparent that one's present moment is also local to this sub-region of fractalesque "space"

Bump.

cowabunga dude

>>7037808
What does that imply?

This thread is cool

>>7037989
that you guys are hella cool.

>implying consciousness is not a complex transformation recursively generated on reflective 2D calabi-yau n-folds

>How characteristic are Julia sets to the complex plane?
>Besides the definition of being the converging points of the iterative formula, what other methods could produce structures that are extremely similar in appearance to Julia sets?
In general, you can use alot of functions. The characteristics come from the fact i^2 = -1.

Let f(x)[0] = x; f(x)[1] = f(x); f(x)[2] = f(f(x)); f(x)[3] = f(f(f(x))) .. and so on.
then f(x)[n] means "x is transformed n times with f". The brackets are in the end because it's easier to read with an actual function.
Lets define lim(n->a) f(x)[n] = f(x)[n->a] (for convenience)

For example here's the formula for a specific point in the mandelbrot transformation:
z^2 + C [n->inf]

This one results in gif related. The animation is changing variable b.
sin(a+bi) [n->inf] = sin(a)*cosh(b) + i*cos(a)*sinh(b) [n->inf]
which is again: sin(sin(sin...(z)...))

This one converges for all z but you can create fractal images by comparing concurrent iterations.
ln(z) [n->inf] = log|z|+arg*i [n->inf]
http://imgur.com/iTl4E5S : the animation is changing some exponent i think

In my opinion is that the brain's visual rendering is somehow heavily relying on complex transformations to handle data. With LSD you can kind of see behind the curtains and see how the circuits in your head work. I dont know shit about complex analysis though. It's very complex.

>>7038199
Are you Dr. John Hollister Titor?