Extracting Beauty From Chaos

There are any number of sites on the World Wide Web dedicated to galleries of computer-generated fractal images. Pictures based on Lyapunov Exponent fractals, such as the one pictured above, are some of the most striking and unusual.

Like most fractal images, Lyapunov Exponent fractals are produced by iterating functions and observing the chaotic behaviour that may result.

In this article, we'll be exploring what Lyapunov exponents are, how you iterate functions, what "chaos" really is, and how you go about turning simple maths into marvellous images. There's also a companion article, Computing the Mandelbrot set by Andrew Williams, which looks at the technical details involved in writing a program to compute the Mandelbrot set.

See:

Box Counting or "Points" on the Strings Length?

That "light Bulb" was the Sun?

Roots, and the Rings of History

Earth's Future in Planetary Observation

On March 31, 2006 the high-resolution gravity field model EIGEN-GL04C has been released. This model is a combination of GRACE and LAGEOS mission plus 0.5 x 0.5 degrees gravimetry and altimetry surface data and is complete to degree and order 360 in terms of spherical harmonic coefficients.

High-resolution combination gravity models are essential for all applications where a precise knowledge of the static gravity potential and its gradients is needed in the medium and short wavelength spectrum. Typical examples are precise orbit determination of geodetic and altimeter satellites or the study of the Earth's crust and mantle mass distribution.

But, various geodetic and altimeter applications request also a pure satellite-only gravity model. As an example, the ocean dynamic topography and the derived geostrophic surface currents, both derived from altimeter measurements and an oceanic geoid, would be strongly correlated with the mean sea surface height model used to derive terrestrial gravity data for the combination model.

Therefore, the satellite-only part of EIGEN-GL04C is provided here as EIGEN-GL04S1. The contributing GRACE and Lageos data are already described in the EIGEN-GL04C description. The satellite-only model has been derived from EIGEN-GL04C by reduction of the terrestrial normal equation system and is complete up to degree and order 150.

Many if interested just have to do a search on Grace in this Bloggery to know the efforts gravitational research has gone to develope the views we have of earth from that magnificent pearl to the dramatic realizations of it's covering above.



ArcGP grid, January 2006 (mGal). Some ERS and ICESat altimetry has been used to fill in some data gaps/errors in the original compilation. (units mGal).Credits: ArcGICE Study Group

A combination of new satellite-derived datasets is providing an exciting opportunity to peer through the sea-ice cover to study circulation patterns in the Arctic Ocean (Forsberg et al., 2006). A better understanding of what's going on beneath the ice will, in turn, lead to a more accurate interpretation of sea-ice thickness data from CryoSat-2.

The new estimates of Arctic Ocean mean dynamic topography have been compiled through a combination of satellite altimetry data from ERS, Envisat and ICESat, and a revised geoid model based on surface, submarine, airborne and satellite gravity field data from the US-German GRACE mission.

Box Counting or "Points" on the Strings Length?

The jump from conventional field theories of point-like objects to a theory of one-dimensional objects has striking implications. The vibration spectrum of the string contains a massless spin-2 particle: the graviton. Its long wavelength interactions are described by Einstein's theory of General Relativity. Thus General Relativity may be viewed as a prediction of string theory! Author Unknown

We understand I think the relevance in regards ot the cosmological views that GR helps us understand in the curvatures inherent as an expression of the cosmos.

What we may have trouble with is the value we may assign such curvatures taken down to the quantum regime. This may seem incompatible, yet, the dynamical nature of the energy is never really that far from speaking from the particle/energy inhernet in nature, as a energy determinant value?

Why would you treat the quantum realm any different then you would the cosmological one, if the assumption is that GR is predicted?



Fractal Dimenison-Tree Silhoutte

I like to think of the "roots and the rings of history" here so that you may see the comparative value of thinking of the "building blocks" not so much as "boxes" but as energy values related to the circle.

There really was a reason to fear pathological entities like the Koch coastline and Peano's monster curve. Here were creations so twisted and distorted that they did not fit into the box of contemporary mathematics. Luckily, mathematics was fortified by the study of the monsters and not destroyed by them. Whatever doesn't kill you only makes you stronger.

Take the Koch coastline and examine it through a badly focused lens. It appears to have a certain length. Let's call it 1 unit. Sharpen the focus a bit so that you can resolve details that are ⅓ as big as those seen with the first approximation. The curve is now four times longer or 4 units. Double the resolution by the same factor. Using a focus that reveals details 1/9 the first focus gives us a coastline 16 times longer and so on. Such an activity hints at the existence of a quantifiable characteristic.

To be a bit more precise, every space that feels "real" has associated with it a sense of distance between any two points. On a line segment like the Koch coastline, we arbitrarily chose the length of one side of the first iterate as a unit length. On the Euclidean coordinate plane the distance between any two points is given by the Pythagorean theorem

Planck time and what new physics would we have shown once we got down to these lengths? The energy of discernation has deluded us into what was once uncertainty has now QGP idealizations and the inherency of the thinking along side of high energy considerations.

Discretium and continuity are not at odds here just that the "realm of thinking" is limited to the GR suppositons about what the world is in cosmological discretium views? Yet, we know at such levels, the "continuity" of the energy has taken over. The coast lines appear fuzzy, yet in "box counting" it doesn't seem that way. What are it's limitations then, when our views meet uncertainty about what discribes the coast line? Shall we now refer to the days, weeks, months, as an energy valuation of the circle, in the trees root and the history it contains?

Pick a "ring/circle" of the tree and tell me what happen during that time?

From Modelling to Experimentation?

Moving to higher energies, the expected fluxes of neutrinos become smaller, that even a cubic kilometer detector is not able to detect them. Larger volumes can be achieved by replacing optical sensors by acoustic detection. The reason is that acoustic waves can propagate over larger distances than light and allow wide spacing of detectors, and therefore larger detector volumes.

From Modelling to new thoughts on experimental processes and approach to the physics involved, it is important that one understands how this approach is considered. Not to loose sight of the relationship to high energy consideration and it's particle shower effect from such interactions.

Without some comprehension of RHIC valuation in production uses what was to be gained from cosmic particle collisions? What future in LHC inclusion of microstate with out some association to particle entities as a result of those collisions?

Reductionist processes leads to comprehension values that if let unnurtured, would not have allowed such model comprehension to exceed current limitation of thinking?

"String theory and other possibilities can distort the relative numbers of 'down' and 'up' neutrinos," said Jonathan Feng, associate professor in the Department of Physics and Astronomy at UC Irvine. "For example, extra dimensions may cause neutrinos to create microscopic black holes, which instantly evaporate and create spectacular showers of particles in the Earth's atmosphere and in the Antarctic ice cap. This increases the number of 'down' neutrinos detected. At the same time, the creation of black holes causes 'up' neutrinos to be caught in the Earth's crust, reducing the number of 'up' neutrinos. The relative 'up' and 'down' rates provide evidence for distortions in neutrino properties that are predicted by new theories."

That "light Bulb" was the Sun?

Plato:

It was important for me to reveal how I am seeing the cosmo. How the superhighway has been spoken too, in regards to the Langrange points.These points are lead to and from unstable orbits. Points, where gravity balances out between bodies, like the earth and the moon. These are not to be considered stable equilibrium points

It was Socrates' turn to look puzzled.
"Oh, wake up. You know what chaos is. Simple deterministic dynamics leading to irregular, random-looking behavior. Butterfly effect. That stuff."
Of course, I know that," Socrates said in irritation. "No, it was the idea of dynamic logic that was puzzling me. How can logic be dynamic

Now surely this is not the case? A "light bulb" is really the sun?

Some Orbits with theirLyapunov Exponents

Maybe just some analogy to what may have become the brilliant idea, was just looking hard enough into what the energy is doing? It found an "avenue or road" to allow for the transferance from "the place," where all ideas reside to become? Hence, "the nature of all things" which already exist, to have found it's way through the mind into a more briliant focus of what was determined of the energy now, becomes, the sun/idea? Worked hard enough to manifest into reality?


Artist's impression of the micro vortices observed in the Northern magnetic cusp by Cluster. It is the first time ever that such phenomenon is observed in space.

So I sit here wondering about where that energy had gone, and how and I am quickly transported back to the conditions of the early universe? "QGP! what you say?" How is that possible?

And from it we see the lagrangian views as points between the sun/earth relation that allow for easier transport(satellites in orbit) then other conditions if gotten into the flow of things?

A State of equilibrium? Que! Non?




Sample Orbits of the Standard Map
(x, y) → (x + y, y − 0.971635 sin (2πx)/2π)Different orbits are assigned different colors.

Nobel Prize in Physics goes too?

AP George F. Smoot, physicist at Lawrence Berkeley National Laboratory, California, (l), and John C. Mather, physicist at NASA Goddard Laboratory for Astronomy and Solar Physics, (r), joint winners of 2006 Nobel Prize for Physics.

Oct. 3 - Americans John C. Mather and George F. Smoot won the 2006 Nobel Prize in physics on Tuesday for work that helped cement the big-bang theory of the universe and deepen understanding of the origin of galaxies and stars.

See:

Smoot Group

Universe Adventure

Formation of the Elements

Anti-Matter in the Universe

If my "predictive qualities" were any good, I would say, "subconsciously" I was picking up on it?:)Oui! Non? See "previous post" to this one.

My "harmonial views and the Law of Octaves" are philosophically embued. So I tend to the "resonances in nature" as a way of looking at the creation of matter states from the origins of the big bang.

So in the "mean time" what can we learn from Nobel Prize Winners. It's a enjoyment to read.

The Periodic Table of the Moon's Strata

Clementine color ratio composite image of Aristarchus Crater on the Moon. This 42 km diameter crater is located on the corner of the Aristarchus plateau, at 24 N, 47 W. Ejecta from the plateau is visible as the blue material at the upper left (northwest), while material excavated from the Oceanus Procellarum area is the reddish color to the lower right (southeast). The colors in this image can be used to ascertain compositional properties of the materials making up the deep strata of these two regions. (Clementine, USGS slide 11)

Clementine gravity experiment used measurements of perturbations in the motion of the spacecraft to infer the lunar gravity field

Like Grace, I choose to build an understanding of the gravity fields.

S-Band Transponder Doppler Gravity Experiment

The gravity experiment used measurements of perturbations in the motion of the spacecraft to infer the lunar gravity field. Clementine was equipped with an S-band microwave transponder and 2 S-band omni-directional high-rate antennas which were used for tracking by the NRL tracking station in Pomonkey, MD, and the NASA Deep Space Network. The frequency of the S-band transmission was measured every 10 sec, and the Doppler shift would give the relative velocity of the spacecraft towards or away from the Earth. Accelerations were calculated from changes in the velocity, and after accounting for the orbit, relative motions of Earth and moon, and Earth and solar gravity, these accelerations are converted to lunar gravity effects on the spacecraft.
The calculated lunar gravity field can be used to model subsurface lunar structure. The Pomonkey station could measure the velocity to an accuracy of 3 mm/sec, while the Deep Space Network stations could achieve about 0.3 mm/sec. Tracking was not possible on most of the lunar far side (120° to 240° long, -45° to 45° lat), when the moon was between the spacecraft and the Earth. In all, over 361,000 observations were made, approximately 57,000 at less than 1000 km altitude.

As our physical interpretation of this lovely pearl(earth) we live on has changed in the conceptual views of "times clocks and such," it became evident in GRACE that the world was quite different then what was first view from space in triumph.

As you might well know, all matter in the universe consists of small particles called atoms and each atom contains electrons that circle around a nucleus. This is how the world is made.
If one places an atom (or a large piece of a matter containing billions and billions of atoms) in a magnetic field, electrons doing their circles inside do not like this very much. They alter their motion in such a way as to oppose this external influence.

Incidentally, this is the most general principle of Nature: whenever one tries to change something settled and quiet, the reaction is always negative (you can easily check out that this principle also applies to the interaction between you and your parents). So, according to this principle, the disturbed electrons create their own magnetic field and as a result the atoms behave as little magnetic needles pointing in the direction opposite to the applied field*.

But of course may I infer "floating ships" over mineral deposits that were conducive to transportation in regards to the superconductors, floating frogs and such? An "attenuator of a kind" for the strength's and weaknesses of such composite gatherings?

But anyway before this "energy is considered in it's matter formed," how did such asymmetrical breaking from the origins not have ocnsidered such constitutions built on the very matters of the moon or such, in it's construction? In the end the gravity field is worth what?

At SLAC and elsewhere in the 1990s, precision measurements probing quantum effects from physics at higher energy scales were very successful. Precision electroweak measurements accurately predicted the mass of the top quark before it was discovered at the Tevatron at Fermilab, and they were cited in the awarding of the 1999 Nobel Prize to Veltmann and t'Hooft, which recognized their work in developing powerful mathematical tools for calculating quantum corrections and demonstrating that the Standard Model was a renormalizable theory. The discovery and mass measurement of the top quark at Fermilab's Tevatron and the precise Z0 boson mass measurement from CERN experiments added to well established values for other Standard Model parameters, to allow predictions for the only Standard Model parameter not yet measured, the Higgs mass.

What is a coupling constant? This is some number that tells us how strong an interaction is. Newton's constant G_N, which appears in both Newton's law of gravity and the Einstein equation, is the coupling constant for gravitational interactions. For electromagnetism, the coupling constant is related to the electric charge through the fine structure constant a


While the idea in my mind is "the extension of all elements demonstrated in some way arising from the standard model, what said that "this element or that" could not have been created from a oscillatory expression of the big bang, and the particles that issue forth, are not without some geometrical expression as "inhernet structures" of that table?



As a "resonantial value" of a point along the length of the string?

Dr. Timmothy Stowe's physicists periodic table



So you see, I had a vision about the future. A time when I will work in space deploying satellites. But what said that future would not ascertain the requirements when our fossil fuels will have to be disregarded? Change the way the planets inhabitants will look forward to the benefits of such conceptual changes?

So this is a fictional posting then, about that future.

CP Violation

The value of non-Euclidean geometry lies in its ability to liberate us from preconceived ideas in preparation for the time when exploration of physical laws might demand some geometry other than the Euclidean. Bernhard Riemann

ON a macroscale the blackhole is a understanding of when we investigate curvature parameters with regards to the nature of our universe in spacetime. We understand this right?

What are the "entropic valuations" being recognized as we look to a earlier time of when the QGP existed and then such manifestaion in the "matters states" have exemplified such characteristics as?


Both space and spacetime can either be curved or flat.

I am going to give you a quick summation of what GR is. It is about "Gravity." Now if you hold that in mind you should not loose any time with what I am telling you.

Now, how is it that we can see the dynamcial nature of the universe, yet, we would not consider the effect of the presence of microstate blackholes in regards to such gatherings in the space, of what we call "spacetime?" What would "such gatherings" show of itself?


A circle of radius r has a curvature of size 1/r. Therefore, small circles have large curvature and large circles have small curvature. The curvature of a line is 0. In general, an object with zero curvature is "flat."

Think about the "circle" and it's 2D view of what the blackhole is doing in 3D +time in context of many blackholes. I always refer to "one" so you can see the comparative view that I am having little success in transferring to you, in what I am seeing.

The curvature parameters are closely associated to the thermodynamic realizations. This is importnat not only on a cosmological level, but on a microstate as well.

Lubos explains that here.

Lubos:

There are lots of other examples what you can do to increase the number of black holes. Change the couplings so that the stars burn their fuel faster, and they will collapse into black hole faster. Reduce the gap between the Planck scale and the QCD scale, and nuclear collisions will be more likely to end up as black holes.

It is quite obvious that the change of virtually any parameter of the Standard Model (plus inflation) in the right direction (one of the two directions) will result in an increase of the number of black holes. How can you doubt such a trivial thing?

So there is something about the nature of our universe and the balance that it seeks to maintain of itself? Here we are, looking at events within the cosmo and "secular views of it's manfiestation" different then other locations within the universe. Yet not apart from it, or not indifferent to it's nature to be part of a larger picture?



Silicon Vertex Tracker. The SVT is the heart of the BABAR experiment at SLAC—in the photo, physicists are putting the finishing touches on improvements to the detector. (Photo Courtesy of Peter Ginter)

SLAC's BaBar collaboration has discovered that CP violation—an asymmetry between the behavior of matter and antimatter—exists even in a very rare class of particle decays. This result offers the most sensitive avenue yet for exploring matter-antimatter asymmetries, with implications for the future understanding of physics beyond the Standard Model.

"BaBar has proven to be a fantastic instrument for exploring the origins of matter-antimatter asymmetries, allowing us to probe with exquisite precision very rare processes related to how the early universe came to be matter dominated," said David MacFarlane, BaBar Spokesperson and Professor at the Stanford Linear Accelerator Center.

So here we are having been given the example of CP violation above and here?

How is it that anything could be asymmetrical? :) So you introduce anti-matter and matter?


(ambigram courtesy John Langdon)

If we could assemble all the antimatter we've ever made at CERN and annihilate it with matter, we would have enough energy to light a single electric light bulb for a few minutes.

As a observer Einstein made it clear that the observable universe has ideas attached to it. The "Pretty girl and the hot stove analogy" was compelling to those of us who recognized the values we may attach to life. "The Gravity of the situation?" How narrow our view of the world is when we feel the world is lost?

But the hope and inspiration is, that the world has a bright future when we undertsand the implications of our views. Our involvement in the "toposense of reality? We are "part and parcel" of it?

So, should we talk about the components of Heaven and Hell( my philosophical discourse on the nature of consciousness?)? You have to understand the picture and the dynamical nature this universe can say about it's entropic valuation?

While I may have understood Omega, it didn't come to the nature it is by not including a geomtrical perspective about the nature of that same universe.

That's my point. It had to arise from a earlier time and the manifestation is the matter states we are defining in correlation to the entropic valuations.

While you see these as macro-characteristics and the relation to blackhole in 3d+time, the result is, a explanation of matter states in "macrostylistic beauty" we see in the events of the cosmo.

If such inclinations to drive the energy to a ever smaller defined circle, as it gets smaller "the difference is" not so indiscernable that the events of the "particle showers" created are matter states that arise form the energy that was used.

You see?:)

The Ceiling

The deeper implications of such a thought from perspective is focused upward? Yet such perspective can be made from other positions? So some minds were flexible? Others, were just engineers? ;)

Understanding other worlds came naturally to him. Perhaps it was an inevitable consequence of being the child of Japanese Americans. His parents, though born in California, spent World War II behind barbed wire, guarded by people with machine guns: incarcerated by their own country as enemy aliens. Afterwards his father worked as a gardener, his mother a maid: two of the few jobs that were available to Japanese Americans. Kaku grew up poor, but one of the family treats was to visit the Japanese Tea Garden in San Francisco's Golden Gate Park. It turned out to be the place of a childhood epiphany. Wondering in the way that only a child does, Kaku looked at the carp swimming in a weedy pond and imagined how they would not be able to conceive of other worlds. "A carp engineer would believe that was all there is; but a carp physicist would see the ripples on the surface and start thinking about unseen dimensions," Kaku told me, laying the first of many lashes on his token engineer.

The "ceiling" is the perspective of the carp, not the perspective of the "carp physicist."

See:

Liminocentric Structures: Which Circle do you Belong Too?-Sunday, July 10, 2005

Ps: Some updates are curvature given for perspective. Think of a string, and any point on that string. What does the energy value of "that point" tell you in regards to the circle? The point on that string. It's just a way of looking at the string and the resonantial value assign along the string's length?

Catching Nature in Action

To capture the particles emerging from powerful proton-proton collisions at the LHC, scientists design and build huge, massive detectors. The CMS detector, about 50 feet tall, relies on an array of particle detection subsystems. The tracker (the subsystem at its core) records particle tracks with ultrahigh precision. The intermediate subsystem, the calorime-ter, determines the energy of the particles escaping the collision. The outermost devices identify muons, heavy electron-like particles that can travel long distances.

Graphic: CMS collaboration

LHCf is a different type of experiment, using the LHC's protons as a source that simulates cosmic rays. It will study how colliding protons cause showers of particles, in particular photons. Analysis of these showers will aid in the interpretation and calibration of large-scale cosmic-ray experiments, which can cover thousands of square kilometers of ground

See:

The wonders of Quark-Gluon Plasma

Quest For Convincing Evidence?

THE BEVALAC IN WHICH IONS OF HEAVY ELEMENTS, CREATED IN THE SUPERHILAC (TOP), WERE SENT DOWN A BEAM PIPE FOR FURTHER ACCELERATION AND EXPERIMENTAL WORK IN THE BEVATRON

WHEN NUCLEI COLLIDE AND THE ENERGY DENSITY OF THE PARTICLES PRODUCED IS SUFFICIENTLY HIGH, THEN A QUARK-GLUON PLASMA COULD BE PRODUCED