help me analyze this chaotic attractor/fractal i designed

reply to post by ImaFungi

......random/chaotic.....

you can get more details about this in my above reply to Indellkoffer.


essentially, most people think CHAOS = NOISE = random chaos and noise are not the same thing.

WRT your question about entropy. there is a theory of molecular kinetics called "autocatakinetics" in which the thermodynamics of an oscillating molecular system are reinforced by the chaotic signal within the system, such that there is zero sum change in entropy (or even net increase of entropy in what might be called negentropy).

so, in other words: yes, a chaotic system has thermodynamic properties different than what is usually generalized by physics.

is the universe (big bang) inherently chaotic (not random)? very probably.
is the 2nd law (flow of entropy) not as strict as "they" would have you believe? i do think so....at least for some systems.

this is the latest render. it is a composite of all 6 (did i say 5 before? oops.) polynomials which i am able to extract from the original iterating function. for all intents and purposes, i think this is as far as these numbers will go.

i will likely find many details in this image that will be worth capturing. i will make them available for anyone interested.



uncompressed image


and, here is a text file containing all 6 of the polynomials which are overlayed to create the above image. you can (probably) plot them on a regular 3D graph. although if you can generate a loop function that will iterate variable z back into z, your result will look more like what i have shown here.

polynomials for composite



....gonna call it a night, guys.

thanks!

reply to post by tgidkp


ok so its like,,,, a star can exhibit its reactions, and shoot off its energy in all directions at all times in a way that can be called chaotic,,, maybe there is no real order to this,, it is just one reaction after the other non stop,,,, this chaotic activity can result in a planet surrounding this sun,, to support mechanisms capable of capturing this suns energy in viable forms,,,,, at this point life version 0.1 the game is crude and simple, but there is need and competition for patterns/efficiency/structure etc.... can it be that decisions ancestors made millions of years ago are the difference between you being a human or a turtle?

the mechanisms that require this suns energy to exist, are now experiencing in live action called life, in which collecting this energy leads to growth, existing for more "time",,, a battle of entropy,,, life is a struggle against decay,, life needs a process to shootgun itself into perpetual growth, or bloomage, to experience itself and copy itself, before it can no longer fight off decay..... the physical biological body of living things is a work of art, a construction,.... the theme of creation is inherent,,, your mind, you are in charge of gaining supplies(nutrients) for your body to construct itself with,,, the outer world is the body you and other minds cooperate to construct to your desires and necessitations,,,, sorry for typeing a bunch of garbage on your thread....... i have a lot of questions and thoughts about these types of topics with little/no text book knowledge...... i see you are getting help from members, and so maybe after you are fininshed with them we can continue to discuss more theoretical and philosophical and realistic theories surrounding some of the things you are discussing ........

also your images look really awesome,,,, you can always make some cash on the side being a modern artist

Originally posted by ImaFungi
if i take a handful of sand, and throw it as hard as i can, is the path the sand takes through the air random/chaotic?

Yes/no as it's a matter of perspective or definition.

There are variables to consider: the shape of your hand, the direction of the wind, gravity, even light's effect on the particles, the shape and size of the individual particles of sand in relation to the particles that they collide with in the air, the weight of the particles... I can't even imagine them all.

reply to post by tgidkp


Beautiful picture. I loves me some fractals! Even the simplest math can create complex looking forms.

reply to post by tgidkp


I see you used the loop function in replace of infinity as a way to interpret the circle.

See, even us non math heads can give input worth using.

reply to post by tgidkp

for all intents and purposes, i think this is as far as these numbers will go.

I think you can go a little farther. What would happen if you reversed all the tag values for all the numbers. Meaning what would happen if you made all the negative numbers positive and all the positives negative.

What about dividing instead of multiplying and multiplying instead of dividing and subtracting instead of adding and adding instead of subtracting?

Would it just give the exact reverse color for every color on the board?

Or would it give exact reverse patterns?

I know nothing of fractal patterns at all but I am interested.

Looks like I have another few weeks of internet research ahead of me.

First exhaustion then the pride that comes with learning a new math.

reply to post by tgidkp


well one of the pictures looks very similar to a pulsar magnetic field diagram,

with the difference in the ratio used not completing to a zero sum,
i am reminded of the indifference of annihilation of matter and anti matter with more matter being the result,

i just read a post about "tiles" used on some religious decorations that are non repeating and expand outwards in ever changing patterns that never repeat

even non liner equations can converge from time to time,
maby find a "prime non liner" number sequence?

ice cracks in thawing ice?

and jellyfish

xploder

Originally posted by ringlejames
reply to post by tgidkp

 

What would happen if you reversed all the tag values for all the numbers. Meaning what would happen if you made all the negative numbers positive and all the positives negative.

that is an extremely astute observation....especially for someone that doesnt quite know what he is talking about!

i was just thinking about this possibility this morning. many of the images that are in the OP are the 'normal' and 'inverse' of the same polynomial.

so, when i say 'inverse', that essentially means what you said in the above quote (in simplest, but inaccurate, terms).


good job.


****TO ALL ---->>> i am in a world of hurt at the moment with regard to my schoolwork. i must, at least until the weekend, postpone any further exposition on this topic. however, this project is far from complete and i hope that you will stick with me.

reply to post by XPLodER


please, a link to the 'religious tiles'? i can probably google the rest.

an extremely helpful post.

Originally posted by tgidkp
reply to post by XPLodER

 

please, a link to the 'religious tiles'? i can probably google the rest.

an extremely helpful post.

i like to help where i can
here is a link to the requested info
link to source

it should be noted that recent developments have shown that in the zero gravity of space that some crystal structures that have formed "while" in zero G have shown this pattern also,

very interesting to think that nearly 500 years ago with out the aid of computer computation, or microscopes (meteorite) to study this non repeating pattern was either instinctive or derived using maths.

anywho
hope this helps you

xploder

Man that looks like fun.
Is there any way of saving the results of each iteration to an array, then later plotting the array?

So much chaos and randomness yet you still end up with beautiful designs.
Yes, designs that were CREATED.
Further proof that life itself is much the same way.

Originally posted by tgidkp

Originally posted by ringlejames
reply to post by tgidkp

 

What would happen if you reversed all the tag values for all the numbers. Meaning what would happen if you made all the negative numbers positive and all the positives negative.

that is an extremely astute observation....especially for someone that doesn't quite know what he is talking about!

Thanks. I have had some fun doing this here at home. Thanks for the push to learn this stuff. I might take sum of the designs I plan on making down to my uncles lithograph shop and see if I cant make a buck or two or three hundred off of some of the ones I am going to create. Dont worry man I am not going to use your images. I take pride in self satisfaction.

Good luck and cant wait to see your future drafts.

this topic intrigues me. i am a math buff of late. i thought I could discover how long the earth with go on for with a scientific calculator. all i could work out was that the universe was laughing at me. Lol

Originally posted by XPLodER
reply to post by tgidkp

 

well one of the pictures looks very similar to a pulsar magnetic field diagram,

with the difference in the ratio used not completing to a zero sum,
i am reminded of the indifference of annihilation of matter and anti matter with more matter being the result,

i just read a post about "tiles" used on some religious decorations that are non repeating and expand outwards in ever changing patterns that never repeat

even non liner equations can converge from time to time,
maby find a "prime non liner" number sequence?

ice cracks in thawing ice?

and jellyfish

xploder

Greetings XPLodER:

Nice seeing you "out there" again... guess we've been running with different packs...

Interesting post.

Here is the pulsar magnetic field diagram you spoke of.

Good call.




S&F OP.

We were thinking along those lines when observing your 'latest' "art."

The immediate, first impression was a certain affinity to these images:









Perhaps this is not a co-inkydink, and it makes all the more interesting the creation of the "inverse" fractals. Looking forward to seeing more of your work.

BTW, the suggestion of turning your images into cash is a good one, IMHO. We like your stuff, and there probably is a market for it. If you don't personally have the time and inclination (being so involved in studies, et al, perhaps consider giving a (decent) piece of the (heretofor zero) potential action to an art rep and sit back and create... oh, and collect the checks.

Peace Love Light
tfw
[align=center][color=magenta]Liberty & Equality or Revolution[/align]

uncompressed image

superhuge WARNING!








hello all, and thanks for sticking around!


as promised, i have been back at my "obsession" this weekend. thanks to those who in the past couple of posts used the language "inverse" and "convergent", i was able to make the next step in this process. so, this thread was a really good idea.

first off, i would like to emphasize that while i am making no small effort to generate pleasing images, i felt like many of my images thus far were lacking in their true purpose. that purpose being, ultimately, an analysis of the complex solutions of the iterating polynomials. those arent just pretty pictures, THOSE ARE NUMBERS! so, the image presented here is a "mathematically correct" representation of the solutions of all six iterated polynomials, plus the inverse sets of those six (total of twelve polynomials).

i have included a z/x (y is the "depth" of the image") axis grid which can be used to identify the positions of the various elements in the graphic according to their real and imaginary coordinates.



please recall from the OP that the iterating functions are inverses of each other. in other words, the quotient of all solutions is -1. also, it is important to see that they do NOT sum to zero.

this translates to the following meaning: the nesting inward of the iterating functions (see the final line in the above image) will only find solutions which satisfy the domain within the domain (within the domain) of the two. this produces a very interesting convergence/divergence pattern in the solution set. an example of this pattern is shown in the following set of number pairs.



in simplest terms, it is far more likely that the proper representation of this function is as a complex manifold or vector space, rather than a fractal proper.

because of this, i have been doing some learning of the quaternions, or hypercomplex numbers, and poincare group. i have been able to find some very surprising implications in the comparison of quaternion analysis and the inital mathematical conditions of this attractor i designed. however, i am way way way out of my league....so go get your math geek friends and tell them to come help me out!

so, it is very likely this is the final 2D rendering of this solution set. as my attentions must now shift.....


.....rather, i would like very much to discuss the nature of the attractor.

i am busy compiling a summary description of the attractor. when i get it up (hopefully by tomorrow evening), i would very much appreciate it if anyone who is well-versed in the trigonometric functions and/or cubic and spherical sections, to jump on board and help me find out just how, exactly, these numbers are doing what they are doing.

believe it or not, i have no idea! an earlier responder made the statement that this chaotic attractor was "created". contrary to this statement, i very much feel as though i am the "recepient" of this information, rather than the originator of it.


i will give a teaser, tho. the attractor increases exponentially toward infinity, from both sides of the x-axis, toward the number (sqrt(3)). my process began as an attempt to formulate a "unit circle" in units of (sqrt(3)), rather than the trigonometric unit circle in (sqrt(1)). the reason for constructing the new unit circle is that the length of the diagonal of a cube is (sqrt(3)).

so, i have generalized the trigonometric functions upward from squareroot 1 -> root 2 -> to root 3. this is a dimensional transformation which i believe will describe the transition of the macrocosm->downward, with the microcosm->upward.


if that doesnt make you think that i am a total nutter, then nothing will!

reply to post by thorfourwinds


hellooooooo
we do seem to miss each other of late,
im glad you added those pics
very interesting pics my friend
xploder

These ARE beginning to be the most complex symmetrical fractals that I have laid eyes on. And the work aint finished by a long shot. Like you said we need more math savvy people here. And I do believe there are another 288 possible images to be made from just one of the polynomials. Now who is the nutter. And I was guessing that you were british I guess I have my answer. Because not only are alot of the people who work with fractals are British, but they are like the only people on earth that use the word nutter.

reply to post by thorfourwinds


i am glad that you saw it too....about the lotus pose. i wasnt going to say anything.

i do like to think that my time and talent is worth money, but i am a big believer in the freedom of information.

for better or worse, the universe always makes sure that i get my due.

reply to post by ringlejames


that is a very specific number.

288?


but really. i am not so interested in making any more images as i am in collecting information.

yeah. this one from today is pretty great. one of the earlier responses said that this function is not complex enough to be a biological model. i think that this could be an ideal model for biological chaos. it definitely reads biology to me, among other things.

no. not British.