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This is a zoom-out of the last image.
This was as far away as the program allowed, unfortunately,
before the picture turned into noise.

[Image: MandDEMalinovsky1b.jpg]
now that is bizarre
a septagonal central medallion,
did you dial that up in the original formula for the fractal?
See the original image......

[Image: cf7c97d0-95dd-46a9-8578-6e6f3d8ff897.jpg]

The septagonal pattern is looking down 90 deg. into the light blue bulb section at the top.
As far as I know, it's due to the fractal formula itself.
I did use an orbit trap coloring method,
but the parameters chosen weren't like
those used for the "pinch" orbit trap mode.

I will definitely experiment to be sure,
and let you know.
OK...I removed the inversion transformation
and further changed the orbit trap coloring method
with another gnarly trap type.

The object view still retained a heptagonal pattern...

The strange thing is that I used a setting that usually
results in almost a noise haze,
but this time...... Reefer

[Image: MandDEMalinovsky2d.jpg]

I was trying zooming into part of the most phantasmagoric area,
and the psychedelic possibilities should prove......fascinating.
Too bad this attempt disappeared......


that looks spectacular for playing into the regrids,
hopefully later tonite.

Looks like a luminescent life form,
and instead of it's place in the Earthly sea,
somewhere in a star factory in space this living thing shall be ...
OK...this is a small zoom into the Malinovsky 3D Mandelbrot.
This is sort of like what had disappeared yesterday......
[Image: MandDEMalinovsky1c.jpg]
Succeeded from failed attempt the other day......

 [Image: MandDEMalinovsky1e.jpg]
your last image is just spectacular
Once again however I went overboard on size and the computer would not handle the load.

I got two segments of a hex in a super large image
at link
[Image: SkJ5eia.jpg?1]

I replicated it all the way in a 5000 by 5000 grid only,
because the 6500 by 6500 just stops working
and a lot just got lost,
so I can supply a half size image of what was left ... for better reference purposes
[Image: 2ZMbCsh.jpg]

let me try again in the next few days, I really like your latest image.
One thing I've tried very recently is a "step size" parameter in the coloring formula.
It significantly smooths rendering a given shape
without losing detail.
I really noticed the improvement in the 12/13 image.
[Image: MandDEMalinovsky1f.jpg]

I keep over convoluting oversized images and it occupies a couple of hours of effort.

So I started over and just went simple

enneagon with hexagons
full size image is huge
[Image: ZQVlO0G.jpg]

interesting there is a flaw ... 
I am uncertain of how that happened

in the center there are 4 mini appendages pointing inwards to the center
between the larger lobes pointing inwards ...
supposed to be 9 of them 


fractal gremlins are at play ...
This is a GIMP test of an earlier image...
I know how lobotomized it was not to have used it before...... Ninja

[Image: MandDEMalinovsky2a.jpg]

V...I've looked at your last image regarding
those anomalies and found they extend into
the very center pattern,
as well as in the outer ring of the repeated pattern.
They're easier to see in the imgur version.

Hmm2 Confused Dunno
yes, very nice,
I am swamped for the next 3 days, then I will have time to try and play with this,
but it will need color enhancements if it works in regrid imaging
The original was run through gimp
but then I ran the gimp image through photobucket...
so take your time...I may redo it again.
Malinovsky/3D Mandelbrot
with various gimp tweaks,
but downsized by photobucket from 1600x1200......

[Image: MandDEMalinovsky2f.jpg]

Incidently, There's a "metallic" setting in a gimp light/shadow-material tab which I'll have to experiment with...... Confused
That symmetry is interesting.
It has a curved vertical symmetry line.
The difference between symmetry reflections in grid replications,
and this type of programmed fractal symmetry is that the resultant symmetry
is more like genetic twins which always have slight differences as humans develop.
There is a lack of sharpness to detail in the last two,
but the bottom half of this one has potential with some color variations.
hope to try one soon
(01-05-2016, 01:57 PM)Vianova Wrote: [ -> ]...
That symmetry is interesting.
It has a curved vertical symmetry line.
The difference between symmetry reflections in grid replications,
and this type of programmed fractal symmetry is that the resultant symmetry
is more like genetic twins which always have slight differences as humans develop.
There is a lack of sharpness to detail in the last two,
but the bottom half of this one has potential with some color variations.
hope to try one soon

OK...this "lack of sharpness".
I can really see a difference between some of the large versions looking sharper than those of other images.
You're citing my last 2 images.
The first one was done with gimp AND photo bucket enhancements,
and the 2nd image was run through gimp only.
I suppose something in the formula parameters might have visible effects though,
but almost impossible (for me anyway) to figure it out. Ninja

I'll have to look into DNA fractals...related to "cellular automata" generations possibly.
Malinovsky formula and coloring...

[Image: MandDEMalinovsky3a.jpg]
That is interesting and looks like a combination of art styles that are blended together.

I had a duifficult time with that one.
huge 5000 by 5000 image just stopped cooperating in process,
had to reduce size and augment with anything available to save it,
and detail was lacking in crispness,
so this was experimental to get an 18 point interior,
you can also take it and reverse color[Image: sXAwM3K.jpg]
"That is interesting and looks like a combination of art styles that are blended together."

I think what you may be seeing is a result of Malinovsky coloring formulas.
Some combinations of internal parameters display strangely abstract alterations
between otherwise symmetrical pairs  of patterns.
They're kind of weird to experiment with because of the arcane uses ascribed to various subroutines
which the programmer has chosen to label with esoteric meanings...
It's possible this "Malinovsky" dreamed it all up
while in a Russian "psychiatric hospital"... Cry
(remember that fractals were once called "monstrous" or "psychopathic" curves in pre computer days)......
Of course, I suspect Kafkaesque qualities to be
part of any mathematician's work over there.

Also, it's impossible to guarantee any kind of symmetry
in a 3D Mandelbrot type object unless it's rotated x,y,z
until it can be positioned 90 degrees over a given pattern center...
one of your earlier fractals from within the last couple of months,
and this is the first 12 sided figure with experimental stuff that went a bit awry,
but it is still a cool but very large image.
I should have left out the central 8 ball unit, it is a complete disaster of splicing,
which happens when you don't magnify enough and try too splice with old eyes.
I got  sloppy, so that is what sloppy looks like in grid replication.
As a small image you can barely see the mess, but in full res Whip    Nonono
There are orther bad splices, 
and the circumferencial 12 extensions got truncated badly in spots
from a sloppy oval cut ... excuses ...  Gangup   
experimental Hmm2
means you can move fast and carelessly to get new methodology recognized and perfected

huge image
[Image: 5vm0Mfk.jpg]


looks like I can also do  a .... 15 sided figure Hmm2

I will try that on the next go
No matter... Wink ...your outer 12-gon is definitely worth it.
One thing I don't understand is how come your images aren't downsized as much as mine.
I am guessing that your images look more sharp and detailed
because your spliced sections were de-magnified first?
Nice effect...... get your bearings on where this next image came from,
scroll to my post of Tuesday, January 5th, 2016, 06:32 am.
THAT bluish construct is s zoom-in from this image...

[Image: MandDEMalinovsky3f.jpg]

 So this NEXT image is a zoom-in from Tuesday, January 5th, 2016, 06:32 am. ...

[Image: MandDEMalinovsky3e.jpg]

As you can see, I way over did the contrast.
Anyway...this next is a zoom-in from above...
...not quite sure where, though...
and the large bee-hive mound in the middle
is especially interesting.
It might be possible to carefully rotate the image
so as to look straight down on the amethyst pattern
of small hives on the mound......

[Image: MandDEMalinovsky3b.jpg]
I was exploring in a side canyon and it increasingly became featureless
I was about to throw it in for the night when I noticed the "distance estimation"
setting was ON...mainly because it's a time saving routine.
When I turned it OFF the image transformed into this...
and it further illustrates the weirdness of Malinovski coloring......

[Image: MandDEMalinovskyexp.jpg]
outrageous images!

I will attempt some regrids in the next couple of days!

Quote:One thing I don't understand is how come your images aren't downsized as much as mine.
I am guessing that your images look more sharp and detailed
because your spliced sections were de-magnified first?

Grid replication makes a small construct enormous.

Be it sqrt 2 rectangle or the golden rectangle {phi},
when the rectangles are replicated,
they push to infinity.

Likewise, any grid reconstruct of a fractal merely is expanded into a geometry.

There are never any "demagnifications",
and actually often, 
resolution is lessened by over replication,
and then I often have to sharpen the resultant final images twice.

To re-cap what I was saying about one of the above...

"It might be possible to carefully rotate the image
so as to look straight down on the amethyst pattern
of small hives on the mound......"

...if I hadn't neglected to save all its settings, that is,
instead of just the image Doh

Something I'd like to know is just what is the effective magnification
of a Mandelbrot set as it's zoomed into. I read back in the '80s
that rendering the entire set would span greater than the orbit of Saturn,
but I don't know that a 3D version is anywhere that big...
something else to search for, I guess......

I looked into SEM operating requirements...
like maintenance costs, etc.
I got the impression a full-time technician
would be needed, and that consumables could be spendy...
plus I imagine the power supply is plenty $$$, too.
I mean, is the idea of getting a working SEM through e-bay
for $1000 too implausible???
My interest stems from a Science Fiction Theater episode I saw a long time ago
in which a scientist "Saw something" in an SEM
but that some peer criticism said it was BS......
sooo... I was thinking Widmannstatten Patterns
and certain fulgurites might prove "interesting"... Hmm2

Quote:I mean, is the idea of getting a working SEM through e-bay

for $1000 too implausible???

highly implausible, leave it on ebay

The SEM I used was very expensive into 6 figures,
and required a science technician staff on hand to keep it running properly,
along with many other high tech apparatus.
They were really good at what they did,
and I was impressed with the young lady that maintainied it.
The team was called Sci-Tech.
It was upon my insistence that they relaxed rules and allowed night work,
so often I had it for hours even past midnite.
Now of course it is completely time taken,
and sign up sheets are full to the brim, 
as I was there during summer quarter when student capacity was at minimum.

Last summer there was quite the fuss about foreign exchange students getting priority time.
Chinese woman... Yak Fu Sue... hogging the SEM time at night.
Pisses me off.

Problems arise in SEM from prior students using the machine and futzing up start settings,
especially chem students readjusting some kind of pressure in the chamber,
and not resetting to the original pressure after usage.
Something like that.
I thought I blew it up once, but it was a pressure relief cap.

I got pretty good at getting high mag close ups,
I think I got a couple in the 20K mag. range.

To have fun with SEM you have to try a variety of mediums.

I was constricted to minerals, and did not have the time to play with this-n-that,
but in retrospect  I wish I had delved into other mediums,
especially organic.

here are progressive close ups from two different sections of a grossular garnet chip. 
left to right ...... bottom right is almost 17K!
large image at link
[Image: 9APvFLK.jpg]

Quote:I was thinking Widmannstatten Patterns

I did a Widmanstatten regrid once ... posted it here years ago,
I'll look for it some day.
nice one,
may be over sharpened.
looks good here on the forum at 175% ...

An experimental design in the replicating template tile.
That would be the ... stacked split section area in the top bulbs, 
and the inner paces between those, both around the perimeter.
huge image
[Image: EfsLFes.jpg]

this won't be up long,
I tried to slip the pentagons into a giant enneagon,
but the computer refused to finish the job in a 6500 by 6500 grid -- it fails

so i tried to recut-n-splice it into a 5000 by 5000
note that the central space has 10 points but is surrounded by an oval placement of small 18 blue oval scepters
[Image: kSGkgEJ.jpg]
They make me think of Byzantine mosaics?
The central pentagonal takes on a lot of depth
If your eye stays fixated on the black center.

This next image is a redo of the first one of the recent set,
but rendered with DE/off to see if it would still plot
reasonably fast.
So it's still a Mbrot/Malinovski type with a Lyapunov coloring formula...
I was surprised to see it worked......

[Image: MandDEMalinovsky3g.jpg]
The world's greatest literature reveals multifractals and cascades of consciousness Holycowsmile
January 21, 2016

Quote:Typical fractals, especially those widely known as the Sierpinski triangle and the Mandelbrot set, are monofractals, meaning that the pace of enlargement in any place of a fractal is the same, linear: if they at some point were rescaled x number of times to reveal a structure similar to the original, the same increase in another place would also reveal a similar structure.

 are more highly advanced mathematical structures: fractals of fractals.

[Image: 160121110913_1_540x360.jpg]
Sequences of sentence lengths (as measured by number of words) in four literary works representative of various degree of cascading character.

[i]Credit: Source: IFJ PAN[/i]

[i]ames Joyce, Julio Cortazar, Marcel Proust, Henryk Sienkiewicz and Umberto Eco. Regardless of the language they were working in, some of the world's greatest writers appear to be, in some respects, constructing fractals. Statistical analysis carried out at the Institute of Nuclear Physics of the Polish Academy of Sciences, however, revealed something even more intriguing. The composition of works from within a particular genre was characterized by the exceptional dynamics of a cascading (avalanche) narrative structure. This type of narrative turns out to be multifractal. That is, fractals of fractals are created.[/i]

As far as many bookworms are concerned, advanced equations and graphs are the last things which would hold their interest, but there's no escape from the math. Physicists from the Institute of Nuclear Physics of the Polish Academy of Sciences (IFJ PAN) in Cracow, Poland, performed a detailed statistical analysis of more than one hundred famous works of world literature, written in several languages and representing various literary genres. 

The books, tested for revealing correlations in variations of sentence length, proved to be governed by the dynamics of a cascade. This means that the construction of these books is in fact a fractal. In the case of several works their mathematical complexity proved to be exceptional, comparable to the structure of complex mathematical objects considered to be multifractal. 

Interestingly, in the analyzed pool of all the works, one genre turned out to be exceptionally multifractal in nature.
Fractals are self-similar mathematical objects: when we begin to expand one fragment or another, what eventually emerges is a structure that resembles the original object. Typical fractals, especially those widely known as the Sierpinski triangle and the Mandelbrot set, are monofractals, meaning that the pace of enlargement in any place of a fractal is the same, linear: if they at some point were rescaled x number of times to reveal a structure similar to the original, the same increase in another place would also reveal a similar structure.

are more highly advanced mathematical structures: fractals of fractals. They arise from fractals 'interwoven' with each other in an appropriate manner and in appropriate proportions. Multifractals are not simply the sum of fractals and cannot be divided to return back to their original components, because the way they weave is fractal in nature. The result is that in order to see a structure similar to the original, different portions of a multifractal need to expand at different rates. A multifractal is therefore non-linear in nature.

"Analyses on multiple scales, carried out using fractals, allow us to neatly grasp information on correlations among data at various levels of complexity of tested systems. As a result, they point to the hierarchical organization of phenomena and structures found in nature. So we can expect natural language, which represents a major evolutionary leap of the natural world, to show such correlations as well. Their existence in literary works, however, had not yet been convincingly documented. Meanwhile, it turned out that when you look at these works from the proper perspective, these correlations appear to be not only common, but in some works they take on a particularly sophisticated mathematical complexity," says Prof. Stanislaw Drozdz (IFJ PAN, Cracow University of Technology).

The study involved 113 literary works written in English, French, German, Italian, Polish, Russian and Spanish by such famous figures as Honore de Balzac, Arthur Conan Doyle, Julio Cortazar, Charles Dickens, Fyodor Dostoevsky, Alexandre Dumas, Umberto Eco, George Elliot, Victor Hugo, James Joyce, Thomas Mann, Marcel Proust, Wladyslaw Reymont, William Shakespeare, Henryk Sienkiewicz, JRR Tolkien, Leo Tolstoy and Virginia Woolf, among others. The selected works were no less than 5,000 sentences long, in order to ensure statistical reliability.

To convert the texts to numerical sequences, sentence length was measured by the number of words (an alternative method of counting characters in the sentence turned out to have no major impact on the conclusions). The dependences were then searched for in the data -- beginning with the simplest, i.e. linear. This is the posited question: if a sentence of a given length is x times longer than the sentences of different lengths, is the same aspect ratio preserved when looking at sentences respectively longer or shorter?

"All of the examined works showed self-similarity in terms of organization of the lengths of sentences. Some were more expressive -- here The Ambassadors by Henry James stood out -- while others to far less of an extreme, as in the case of the French seventeenth-century romance Artamene ou le Grand Cyrus. However, correlations were evident, and therefore these texts were the construction of a fractal," comments Dr. Pawel Oswiecimka (IFJ PAN), who also noted that fractality of a literary text will in practice never be as perfect as in the world of mathematics. It is possible to magnify mathematical fractals up to infinity, while the number of sentences in each book is finite, and at a certain stage of scaling there will always be a cut-off in the form of the end of the dataset.

Things took a particularly interesting turn when physicists from the IFJ PAN began tracking non-linear dependence, which in most of the studied works was present to a slight or moderate degree. However, more than a dozen works revealed a very clear multifractal structure, and almost all of these proved to be representative of one genre, that of stream of consciousness. LilD The only exception was the Bible, specifically the Old Testament, which has so far never been associated with this literary genre.

"The absolute record in terms of multifractality turned out to be Finnegan's Wake by James Joyce. The results of our analysis of this text are virtually indistinguishable from ideal, purely mathematical multifractals," says Prof. Drozdz.
The most multifractal works also included A Heartbreaking Work of Staggering Genius by Dave Eggers, Rayuela by Julio Cortazar, The US Trilogy by John Dos Passos, The Waves by Virginia Woolf, 2666 by Roberto Bolano, and Joyce's Ulysses. At the same time a lot of works usually regarded as stream of consciousness turned out to show little correlation to multifractality, as it was hardly noticeable in books such as Atlas Shrugged by Ayn Rand and A la recherche du temps perdu by Marcel Proust.

"It is not entirely clear whether stream of consciousness writing actually reveals the deeper qualities of our consciousness, or rather the imagination of the writers. It is hardly surprising that ascribing a work to a particular genre is, for whatever reason, sometimes subjective. We see, moreover, the possibility of an interesting application of our methodology: it may someday help in a more objective assignment of books to one genre or another," notes Prof. Drozdz.
Multifractal analyses of literary texts carried out by the IFJ PAN have been published in Information Sciences, a journal of computer science. The publication has undergone rigorous verification: given the interdisciplinary nature of the subject, editors immediately appointed up to six reviewers.

Story Source:
The above post is reprinted from materials provided by The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of SciencesNote: Materials may be edited for content and length.

Journal Reference:

  1. Stanisław Drożdż, Paweł Oświȩcimka, Andrzej Kulig, Jarosław Kwapień, Katarzyna Bazarnik, Iwona Grabska-Gradzińska, Jan Rybicki, Marek Stanuszek. Quantifying origin and character of long-range correlations in narrative textsInformation Sciences, 2016; 331: 32 DOI: 10.1016/j.ins.2015.10.023

Cite This Page:
The Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences. "The world's greatest literature reveals multifractals and cascades of consciousness." ScienceDaily. ScienceDaily, 21 January 2016. <>.

[i]It writes itself.[/i]
[i]It Rights itself.[/i]
[i]Itza Fractal itself?[/i]

[i]Brain study suggests consciousness a matter of optimal degree of connectedness in neural network

January 27, 2016 by Bob Yirka report

[i][Image: brain.jpg]
White matter fiber architecture of the brain. Credit: Human Connectome Project.
(Medical Xpress)—A team of European researchers has found evidence that suggests that human consciousness is a state where the neural network that makes up the brain operates at an optimal degree of connectedness. In their paper published in [i]Journal of the Royal Society Interface, the team describes their study of the human brain using volunteers undergoing fMRI scans while succumbing to the effects of an anesthetic that caused them to lose consciousness, and what was revealed in reviewing the scan data.

Human beings, when awake, exist in a state of consciousness that is uniquely difficult to define.(fractal and multifractal?) Scientists try by agreeing that it is the ability to have subjective experiences and to enjoy a first-person perspective on the "reality" of the world. [/i][/i]

[i][Image: 220px-Animation_of_the_growth_of_the_Man...finity.gif][/i]
[i]But that does not explain the voice that is our own self, nor the varying degrees of consciousness, such as the differences between being asleep, versus partially awake, versus being completely unconscious. In this new effort, the researchers sought to learn more about the state that exists in the mind when consciousness occurs by enlisting the assistance of 12 volunteers who agreed to be made unconscious by the drug propofol, normally used to put people under during surgical procedures (and notably, also the drug that led to the death of singer Michael Jackson) while undergoing fMRI scans.[/i]

[i]Scientists (and surgeons) believe that propofol causes people to become completely unconscious, which by definition would mean to become incapable of processing thoughts. The brain should not be able to process pain signals, for example, thus making surgery a pain free experience. To gain a better perspective on the various states of consciousness, the team watched blood flow changes in the brains of the volunteers as they moved from a conscious state, to unconsciousness and then back to consciousness.[/i]

In studying the scans, the researchers found that when the volunteers were conscious, there was what they describe as "a flurry of ever-changing activity," with a lot of activity between the various neural networks. In contrast, they found that while unconscious, the brains of the volunteers were engaged in far less interconnectivity and were less variable over time.

These findings, the team suggests, show that consciousness in the brain is merely, in a physical sense, a state where there is an optimal level of neural network connectedness.

[Image: 1x1.gif] Explore further: Psychologists report new insights on human brain, consciousness

More information: Enzo Tagliazucchi et al. Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics, Journal of The Royal Society Interface (2016). DOI: 10.1098/rsif.2015.1027

Loss of cortical integration and changes in the dynamics of electrophysiological brain signals characterize the transition from wakefulness towards unconsciousness. In this study, we arrive at a basic model explaining these observations based on the theory of phase transitions in complex systems. We studied the link between spatial and temporal correlations of large-scale brain activity recorded with functional magnetic resonance imaging during wakefulness, propofol-induced sedation and loss of consciousness and during the subsequent recovery. We observed that during unconsciousness activity in frontothalamic regions exhibited a reduction of long-range temporal correlations and a departure of functional connectivity from anatomical constraints. A model of a system exhibiting a phase transition reproduced our findings, as well as the diminished sensitivity of the cortex to external perturbations during unconsciousness. This framework unifies different observations about brain activity during unconsciousness and predicts that the principles we identified are universal and independent from its causes. 

[i]Journal reference: Journal of the Royal Society Interface[/i]
That is really interesting on the multifractals and consciousness.
Exponential consciousness.

Quote:....... a detailed statistical analysis 
of more than one hundred famous works of world literature, 
written in several languages and representing various literary genres. 

..... advanced equations and graphs 
are the last things which would hold their interest, 
but there's no escape from the math. 

.... the construction of these books is in fact a fractal. 
......their mathematical complexity proved to be exceptional, 
comparable to the structure of complex mathematical objects, 
considered to be multifractal. 

... a dozen works revealed a very clear multifractal structure,
that of stream of consciousness.

I get that mile high tsunami surge stream of consciousness,
when I power binge on harmonic number code systems.
That is when I am in Clear Light mode, in universal harmonic code.

This happens when I get an important number value ... like an angle or constant etc,
and I work it on the calculator with a rapid fire succession of number extrapolations.

This has to flow largely from the intuitive consciousness
to expand exponential equation flow to the target value.
The direction of the number testing is guided by an intent 
to employ what they called "multi fractal consciousness".

So, often I will engage in a project for a week straight,
when the energy creates "cascades of consciousness" in Clear Light mode.

I just did that for the last week, which is why I haven't been here much.
Something called the Cabibbo angle.
Then another physics number code multifractal called the Weinberg angle.
I did very very well. 

The harmonic number code practice during exponential consciousness cascade-a-thons,
over the years adds up and you get pretty good at it.
Each new catalytic harmonic number code consciouness event,
builds upon all the previous number code satori work ethic Lol
and as such,
the experience of Clear Light mode in Universal Harmonic code is spiritual in context.
I don't use physics methods, 
but I use pure modern tetrahedral and phi geometry in complex applications.

Harmonic code ...   isn't quantum or nuclear physics.

But it is thermodynamic!  Split_spawn

Physics is for the Big Boys that do physics Whip

I am the Psychedelic Smoke Kingpin of Worship Universal Harmonic Code 

Most scientists and physicists don't like harmonic code.
They look at it as ... artsy fartsy math.

You can present them a nuclear Da Vinci melting in pi meson and quark soup,
with over 10 decimal accuracy,
using modern constants like pi and phi and the fine structure constant ...
and they will just go Nonono
because you painted a mathematical masterpiece,
on a super conscious canvas of harmonic code.

physicists vs Is-a-cists Hmm2

The result of the last week "cascade of number code consciousness"
is that I now can quantum astro surf the Cabibbo angle tangent,
right back into modern tetrahedral and phi geometry.

In the standard geometry,
I finally got to a tetrahedral tangent that had eluded me for awhile.
The tetrahedral angle tangent,
sqrt 2
54.73561032 degrees,
What is the tangent of 54.73561032 / by 2 = 27.36780516 degrees ? 
It was a bitch of a tangent.
There are several combinations of tetrahedral and in this case, with sqrt 3 functions,
that will isolate the tangent,
and they are as convoluted as brain fuck in a k-hole Reefer

To use the goddam tangent effectively you need the simplest possible combination
of tetrahedral components in the convoluted fraction.
Otherwise it is a number code {ketamine} k-hole tangent.

This was the best that I could come up with, and it was a nasty tussle to get it this compact.

tangent 27.36780516 degrees = {sqrt 12 minus two} / by square root 8.
As improv is as is was 
we can now compare the multi-fractal stream of consciousness to semantics.

I wonder?

Do Aliens communicate via multi-fractal channels?


[Image: cf7c97d0-95dd-46a9-8578-6e6f3d8ff897.jpg]

Semantically speaking: Does meaning structure unite languages?

February 1, 2016

[Image: language.jpg]

Credit: Paul Brennan/public domain

We create words to label people, places, actions, thoughts, and more so we can express ourselves meaningfully to others. Do humans' shared cognitive abilities and dependence on languages naturally provide a universal means of organizing certain concepts? Or do environment and culture influence each language uniquely

Using a new methodology that measures how closely words' meanings are related within and between languages, an international team of researchers has revealed that for many universal concepts, the world's languages feature a common structure of semantic relatedness.
"Before this work, little was known about how to measure [a culture's sense of] the semantic nearness between concepts," says co-author and Santa Fe Institute Professor Tanmoy Bhattacharya. "For example, are the concepts of sun and moon close to each other, as they are both bright blobs in the sky? How about sand and sea, as they occur close by? Which of these pairs is the closer? How do we know?"
Translation, the mapping of relative word meanings across languages, would provide clues. But examining the problem with scientific rigor called for an empirical means to denote the degree of semantic relatedness between concepts.

To get reliable answers, Bhattacharya needed to fully quantify a comparative method that is commonly used to infer linguistic history qualitatively. (He and collaborators had previously developed this quantitative method to study changes in sounds of words as languages evolve.)
"Translation uncovers a disagreement between two languages on how concepts are grouped under a single word," says co-author and Santa Fe Institute and Oxford researcher Hyejin Youn. "Spanish, for example, groups 'fire' and 'passion' under 'incendio,' whereas Swahili groups 'fire' with 'anger' (but not 'passion')."
To quantify the problem, the researchers chose a few basic concepts that we see in nature (sun, moon, mountain, fire, and so on). Each concept was translated from English into 81 diverse languages, then back into English. Based on these translations, a weighted network was created. The structure of the network was used to compare languages' ways of partitioning concepts.
The team found that the translated concepts consistently formed three theme clusters in a network, densely connected within themselves and weakly to one another: water, solid natural materials, and earth and sky.
"For the first time, we now have a method to quantify how universal these relations are," says Bhattacharya. "What is universal - and what is not - about how we group clusters of meanings teaches us a lot about psycholinguistics, the conceptual structures that underlie language use."
The researchers hope to expand this study's domain, adding more concepts, then investigating how the universal structure they reveal underlies meaning shift.
Their research was published today in PNAS.
[Image: 1x1.gif] Explore further: Humans innately impose grammatical structure on to languages that they learn, suggests research
More information: On the universal structure of human lexical semantics, 
Journal reference: Proceedings of the National Academy of Sciences[Image: img-dot.gif] [Image: img-dot.gif]
Provided by: Santa Fe Institute

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Quote:"What is universal - and what is not - about how we group clusters of meanings teaches us a lot about psycholinguistics, the conceptual structures that underlie [url=]language use."

psycholinguistics  LilD

[Image: MandDEMalinovsky2a.jpg]
EA......some of the terms in that multi/monofractal article   I think I've seen referred to as
"space filling curves curves", and as a basis for analyzing the stock market (the fractal involved draws simulated mountain ranges).
I looked into "multifractals" and turned up a fractal analysis program...FracLac...that's apparently avaialable.

They had some revealing Henon mapping images generated by FracLac...
that I've only seen  rendered before in a crude C-64 program
wherein formula parameters were tweaked by game paddle potentiometers!
What I had seen previously reminded me of the chaotic zones of stability in gravitational Lagrange Points
...or so I imagined Reefer

 Will look more into it......