help me analyze this chaotic attractor/fractal i designed

reply to post by tgidkp


This is some pretty intriguing research! I will be keeping a close eye on your future posts and threads

because of the last fractal/polygon image i posted, i was able to make the connection that the "flat" fractal is a 3 dimensional shape.

i hypothesized that IF the polygon and fractal are correlated, then if i rotate the polygon 45degrees on the diagonal z/y, i will see the hexagon face. likewise, if i rotate the fractal by the same factor, i should see a hexagonal transformation.

sure enough. i have posted my initial results below. this fractal IS INDEED able to be rotated. i would be fascinated to see an animation of such a rotation, but i think that is waaaay over my head! however, i will continue to render all polynomials at the new angle.

in the image below, the "cross" is located at 3.925ish and the hex shape is located at 4.618. there are total 4 crosses (labeled). when these crosses are rotated, they become the hexagonal form. can you see how that rotation is happening?

reply to post by tgidkp


I'll have to look in greater detail when I have a moment in order to contribute something thats more useful. But I am quite familiar with fractals and they were used by my first company in the 1980's to take biometric information in the form of fingerprints and use the very limited processing speed and circuit design we had at the time to both store raw identification data and access it very rapidly. It also allowed a form of variable and adaptive encryption thats still classified. We all have heard that a picture is worth a thousand words, it can also offer a far greater perspective. Fractals are constructs that encrypt information in an extraordinarily efficient modality.

Your interest in bioinformatics is intriguing (also one of my areas of passion and work) because nature uses what we call encryption not so much as to hide information, though we know that Dolphins actually do just that. But its used to optimize bio-informatic communication in everything from the brain to sonar (bats and marine mammals) as well as ways of using visual optimization of images (why people are so good at teasing out the nuances of image intelligence, as well as the subtle linguistic analysis so that even after the computers sift threw signal intelligence for key words dates etc, and other things I can't go into at some point some person has to get involved in the process of determination, steps above just analysis.

With a fractal because they are infinitely variable in size-perspective, a small fractal based sample of a small area like a field of grain to a forest, you can determine the number of total grain or trees in that environment. Using a fractal determinant in areas like social media, or natural events, or landscape its possible to get a tremendously accurate planet wide picture of things that can be visually defined, and thats fractals.

I use fractals as ways to take non-visual constructs and convert them into tremendous "snap shots" whose data is rapidly understood, a lot simpler then a row of equations.

Have to get back to work, people like to get paid, but I will follow-up on a very interesting and useful field. Best of luck, and I'll get back to you soon.

reply to post by tgidkp


I can somewhat imagine what that image may look like in 3D, but it's a bit complicated to put into a 3D modeling program. I'm used to working with simpler shapes.

I can't tell by looking at it if the curves are flat (xy only), or if they're helical (stretched along the z-axis as well). Is there no way to render a perspective view?

reply to post by circlemaker


the depth of the image in the z/x plane is given by the coloring algorithm. the name of the algorithm is "angle to origin". so, in other words, points in the field with the same coloring are at an equal angular distance from the z/y plane. it is not easy to see this thing in 3D, but i am beginning to get a glimpse of it.

i am going to work on getting better imaging of the fully rotated form.

reply to post by tgidkp


That is about the coolest fractal pic I've ever seen.

It seems to have significance, as if it was a symbol rather than a visualized math function.

reply to post by arbiture


wow! welcome! what a fascinating post.

now THAT is something that i can start looking into.....for reals.


the purpose of these images is, as you have clearly pointed out, to understand the underlying organization of number field from whence they came. i could tell very early on in this project that the data was showing peculiar relationships. but it was not until i was able to render the solutions visually that i could begin to understand.

and i am truly only just beginning.


thanks a lot, man. the process data that i have given in this thread is a bit of a mess.....and communicating over the net complicates things further, but if you want to talk through some of this, i would be very happy.

reply to post by ExShill


yes. i agree. this is the reason that i am spending every waking and spare moment of my days examining it.

reply to post by tgidkp


Thank you for the kind compliment. As for having "peculiar data" I have to look at this from several points of view. First look at the data set, including represented as a fractal there may be numerous things to consider. When data looks "odd" that may mean an incongruity with other aspects of the data. The odd data may represent a visualization of not-immediently-apparent conflict with other data sets just an artifact of another part of the said data. Just as one logarithmic equation can be isolated and address several aspects of the whole, you may be seeing the localized process of a point, structural aspects, the structure that provides robustness to the whole. It just is not as obvious as it may not be , alone, a data subset but an overall data architecture, or multi-dimension geo-spacial (3D) and topological (2D aspect) of the information.

Fractals require an enhanced flexibility in seeing the whole structure. And a fractal is unique because of its information encoding thats not scale dependent. I have used "layered and off set" fractals that can be stacked in 2D format one on top of another, but each of the same fractal is off set the "center" aspect of the same fractal offering numerous types By there very nature fractals are an ultra-dense but very pliable in data storage or analysis.

I have a nice CGI VR "room" that permits objects to appear to float in mid air. And for a many of images the thousands of image/sound projector's allow an image to be "played upon" an area in the room by setting up an interference pattern, any were and in multiple places in this room. For very dense and detailed images I still need the VR/CGI goggles. My cat won't go near that room when I take him to the office. Soon we should be able to project a television/video like field allowing the ability to place video/audio transmissions anywhere in the room. But toys aside, today I use it to get an "all aspect" view of things like fractals and chemistry and biological structure from an encrypted informatics visual and auditory "signature". Keeping in mind in nature things are encrypted for optimization and robustness, rarely for subterfuge.

One thing that has helped me, by opening my abilities to perceive information in multiple ways is to design and build a technology in this room that uses synthetic synesthesia. I can understand more then data but information, that combines the objective as well as the subjective " personality" What I never expected was that each of us can see the same "data"but how we read that is unique to individuals. I have my own people look, hear and feel the same visual information construct that I do, but each person can take a different aspect of the same presentation and "feel" insight or a eureka moment thats individualistic. Just as we all get something different by looking at the Mona Lisa for example. Oh we all see the same painting, we can agree on painting styles pigment and canvas composition. But what it means to each person has given me insight I never would have had.

Will get back to you again soon, this is a field I love to discuss as its ability to both quantify and store huge amounts of data is amazing.

Originally posted by tgidkp
because of the last fractal/polygon image i posted, i was able to make the connection that the "flat" fractal is a 3 dimensional shape.

i hypothesized that IF the polygon and fractal are correlated, then if i rotate the polygon 45degrees on the diagonal z/y, i will see the hexagon face. likewise, if i rotate the fractal by the same factor, i should see a hexagonal transformation.

sure enough. i have posted my initial results below. this fractal IS INDEED able to be rotated. i would be fascinated to see an animation of such a rotation, but i think that is waaaay over my head! however, i will continue to render all polynomials at the new angle.

in the image below, the "cross" is located at 3.925ish and the hex shape is located at 4.618. there are total 4 crosses (labeled). when these crosses are rotated, they become the hexagonal form. can you see how that rotation is happening?

from an optical physics angle i can say that this latest pic is consistent with a complex paraberla,
a focal point and a recipercal convergence point,
i would suggest while within an encompasing optical media environment

very intereseting from a focal point of view

xploder

Firstly I know nothing about higher maths so I am just playing!

Took the second algorithm you put up and inserted the golden mean for each of the constants. Seeing as you are looking at chaos, There is nothing more chaotic than the golden mean (1.618).

I don't have any cool software so I put it into excel and tried to tidy it up.

This is what I got

=((-32768/1.618^8)*(1.618+3^8)-(7.99999999999*1.618^7)*(1.618+3*1.618+3^7)+(27.9999999999*1.618^6)*(1.618+3^6)*(1.618^2)+(6*1.618+4.42857142856-55.999 9999998*1.618^5)*(1.618+3*1.618+3^5)*(1.618^2+6*1618-4.71428571431+69.9999999998*1.618^4)*(1.618+3^4)*(1.618^4+12*1.618^3)+(26.5714285714*1.618^2)-(56 .5714285717*1.618-85.4000000001-55.9999999998*1.618^3)*(1.618+3*1618+3^3)*(1.618^4+12*1618^3+8.28571428561*1.618^2)-(166.285714286*1.618+71.8571428579 +27.9999999999*1.618^2)*(1.618+3^2)*(1.618^6+18*1618^5+66.4285714284*1.618^4)-(282.857142859*1.618^3)-(1281*1618^2)+(1293.42857144*1.618+2525.57142858 -7.99999999995*1.618*1.618+3*1.618+3*1.618^2)+(6*1618-23.0000000001*1.618^4)+(12*1618^3)-(10.0000000001*1.618^2)-(276.000000001*1.618+273.000000002+0. 999999999993*1.618^8)+(24*1618^7)+(124*1618^6)-(792.000000004*1.618^5)-(5978.00000001*1.618^4)+(12072.0000001*1.618^3)+70716.0000002*1.618^2)-(150696. 000001*1.618-23774.9999996)

= 6.98071E23

Don't know if this means anything to you. If it does I would love to know what because I don;t have a clue.

But just on a side line I have been using this same ration to facture perception as a levelerin risk management and it seems to work well. So I like the golden mean, it's naturally useful!

Scratch that, just noted I left a couple of .'s out of the 1.618 so became 1618.

=((-32768/1.618^8)*(1.618+3^8)-(7.99999999999*1.618^7)*(1.618+3*1.618+3^7)+(27.9999999999*1.618^6)*(1.618+3^6)*(1.618^2)+(6*1.618+4.42857142856-55.999 9999998*1.618^5)*(1.618+3*1.618+3^5)*(1.618^2+6*1618-4.71428571431+69.9999999998*1.618^4)*(1.618+3^4)*(1.618^4+12*1.618^3)+(26.5714285714*1.618^2)-(56 .5714285717*1.618-85.4000000001-55.9999999998*1.618^3)*(1.618+3*1618+3^3)*(1.618^4+12*1618^3+8.28571428561*1.618^2)-(166.285714286*1.618+71.8571428579 +27.9999999999*1.618^2)*(1.618+3^2)*(1.618^6+18*1.618^5+66.4285714284*1.618^4)-(282.857142859*1.618^3)-(1281*1.618^2)+(1293.42857144*1.618+2525.571428 58-7.99999999995*1.618*1.618+3*1.618+3*1.618^2)+(6*1.618-23.0000000001*1.618^4)+(12*1618^3)-(10.0000000001*1.618^2)-(276.000000001*1.618+273.000000002 +0.999999999993*1.618^8)+(24*1618^7)+(124*1618^6)-(792.000000004*1.618^5)-(5978.00000001*1.618^4)+(12072.0000001*1.618^3)+70716.0000002*1.618^2)-(1506 96.000001*1.618-23774.9999996)

Now have 6.98949E+23

I found a free fractile generator online. and put this number in. The result I got looks like an egg!!! with a black space in the middle that sort of looks like a bulls head!!. Saying that it does bearing a striking resemblance to a womb!! weird!!

Oh well it was a fun half hour!

did i forget to upload the new images of the rhombic-dodecahedron? whoops.

i am so glad i made this thing. it really helps to see all of these numbers in three (four?) dimensions.

for those who are interested:

long blue line = ((1+sqrt(5))/2) = golden mean
short blue = ((1+sqrt(5))/2)-1
red = (sqrt(2)/2)+(sqrt(3)/2)
green = sqrt(2)
yellow = .5*sqrt(3)

i took the photos at a perspective length of ~10 feet....so the angles and lengths should be very accurate. also, i have discovered that face-on is not quite the way to look at this thing. the most interesting ratios of lengths come from viewing at a vertice down its line. i have taken pictures of this very complex projection and the results are impressive! i will get those up at some point.

rhombic face



square face



hexagonal face





..................

.....what is really hilarious is that, while i was writing up this post i realised that i did not know what the length of the short and long blue segments are. so i messed around a bit and looked at the book.

originally, when i built the standard cube, i used the mid-length blue lines to represent length of '1'. the other ratios came out correct, so i went with that....and mid-blue has been the unit base for this shape (reference the pictures from a couple weeks ago when the cube part was attached. the cube is built from two-jointed mid-length blues, which equates to a side length for the cube of '2'.

....but what i just figured out is that it is not really a unit of 1. more properly, it is:

( (1+sqrt(5))/(2) ) - ( ( (1+sqrt(5))/(2) ) -1 ) = 1
or
( ( ( (1+√(5))/(2) ) - ( ( (1+√(5))/(2) ) ) ) -1 = -1

**** 1 OR -1 ***** (note the location of parenthesis above)


so. the reason that the formulas which i have been producing have given themselves so well to projection on the complex plane is that the functions are based on the complex unit 'i'!



if we extend this idea out to the trigonometric unit circle, we must come to the same conclusion, which is this:

the unit circle is NOT based on unit of 1.
the unit circle IS based on unit of the differences of the golden ratio as shown above, ultimately producing units of sqrt(1) AND sqrt(-1).


i may have to go back and revise some of my formulas.

reply to post by tgidkp


It reminds me of this:




Never ending knot. Well only the first few made me think of this.

Anyways, I read this book lately (about the Universe being all information, one and two, so in essence all is deterministic as true random events can't be compressed into info which is a level lower) and he stated that life exploits entropy. Life itself is structure but it creates enough entropy to "satisfy" the Universe's need for an increasing total entropy (that is, if we are correct with the assumption that net entropy increases over time).

So even though I can't give you any mathematical hints for finding you biological strange attractor, maybe the above is of any value?

Originally posted by JakiusFogg
Scratch that, just noted I left a couple of .'s out of the 1.618 so became 1618.

=((-32768/1.618^8)*(1.618+3^8)-(7.99999999999*1.618^7)*(1.618+3*1.618+3^7)+(27.9999999999*1.618^6)*(1.618+3^6)*(1.618^2)+(6*1.618+4.42857142856-55.999 9999998*1.618^5)*(1.618+3*1.618+3^5)*(1.618^2+6*1618-4.71428571431+69.9999999998*1.618^4)*(1.618+3^4)*(1.618^4+12*1.618^3)+(26.5714285714*1.618^2)-(56 .5714285717*1.618-85.4000000001-55.9999999998*1.618^3)*(1.618+3*1618+3^3)*(1.618^4+12*1618^3+8.28571428561*1.618^2)-(166.285714286*1.618+71.8571428579 +27.9999999999*1.618^2)*(1.618+3^2)*(1.618^6+18*1.618^5+66.4285714284*1.618^4)-(282.857142859*1.618^3)-(1281*1.618^2)+(1293.42857144*1.618+2525.571428 58-7.99999999995*1.618*1.618+3*1.618+3*1.618^2)+(6*1.618-23.0000000001*1.618^4)+(12*1618^3)-(10.0000000001*1.618^2)-(276.000000001*1.618+273.000000002 +0.999999999993*1.618^8)+(24*1618^7)+(124*1618^6)-(792.000000004*1.618^5)-(5978.00000001*1.618^4)+(12072.0000001*1.618^3)+70716.0000002*1.618^2)-(1506 96.000001*1.618-23774.9999996)

Now have 6.98949E+23

I found a free fractile generator online. and put this number in. The result I got looks like an egg!!! with a black space in the middle that sort of looks like a bulls head!!. Saying that it does bearing a striking resemblance to a womb!! weird!!

Oh well it was a fun half hour!

Greetings:

Good on you!

However, actually, we are a bit taken aback, considering your status here...

No pics - didn't happen...

You, of all people, should 'know' that.

However, we still love you.

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