--- On

**Mon, 2/21/11, George T. Pantos**wrote:*<gop6@...>*

From: George T. Pantos <gop6@...>

Subject: [hameltech] Particles That Flock Strange Synchronization Behavior at the Large Hadron Collider Scientific American

To: hameltech@yahoogroups.com, 4DWorldx@yahoogroups.com

Date: Monday, February 21, 2011, 8:47 PMFrom Wikipedia, the free encyclopediaThis article **is missing citations or needs footnotes**. Please help add inline citations to guard against copyright violations and factual inaccuracies.*(May 2009)*The**Sierpinski triangle**(also with the original orthography*Sierpiński*), also called the**Sierpinski gasket**or the**Sierpinski Sieve**, is a fractal and attractive fixed set named after the Polish mathematician Wacław Sierpiński who described it in 1915. However, similar patterns appear already in the 13th-century Cosmati mosaics in the cathedral of Anagni, Italy.^{[1]}Originally constructed as a curve, this is one of the basic examples of self-similar sets, i.e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction.Comparing the Sierpinski triangle or the Sierpinski carpet to equivalent repetitive tiling arrangements, it is evident that similar structures can be built into any rep-tile arrangements.## Contents

## [edit] Construction

An algorithm for obtaining arbitrarily close approximations to the Sierpinski triangle is as follows:- Start with any triangle in a plane (any closed, bounded region in the plane will actually work). The canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis (first image).
- Shrink the triangle to ½ height and ½ width, make three copies, and position the three shrunken triangles so that each triangle touches the two other triangles at a corner (image 2). Note the emergence of the central hole - because the three shrunken triangles can between them cover only 3/4 of the area of the original. (Holes are an important feature of Sierpinski's triangle.)
- Repeat step 2 with each of the smaller triangles (image 3 and so on).

Note that this infinite process is not dependent upon the starting shape being a triangle—it is just clearer that way. The first few steps starting, for example, from a square also tend towards a Sierpinski triangle. Michael Barnsley used an image of a fish to illustrate this in his paper "V-variable fractals and superfractals."^{[3]}The actual fractal is what would be obtained after an infinite number of iterations. More formally, one describes it in terms of functions on closed sets of points. If we let*d*_{a}note the dilation by a factor of ½ about a point a, then the Sierpinski triangle with corners a, b, and c is the fixed set of the transformation*d*_{a}U*d*_{b}U*d*_{c}.This is an attractive fixed set, so that when the operation is applied to any other set repeatedly, the images converge on the Sierpinski triangle. This is what is happening with the triangle above, but any other set would suffice.If one takes a point and applies each of the transformations*d*_{a},*d*_{b}, and*d*_{c}to it randomly, the resulting points will be dense in the Sierpinski triangle, so the following algorithm will again generate arbitrarily close approximations to it:Start by labelling**p**_{1},**p**_{2}and**p**_{3}as the corners of the Sierpinski triangle, and a random point**v**_{1}. Set**v**_{n+1}= ½ (**v**_{n}+**p**_{rn}), where r_{n}is a random number 1, 2 or 3. Draw the points**v**_{1}to**v**_{∞}. If the first point**v**_{1}was a point on the Sierpiński triangle, then all the points**v**_{n}lie on the Sierpinski triangle. If the first point**v**_{1}to lie within the perimeter of the triangle is not a point on the Sierpinski triangle, none of the points**v**_{n}will lie on the Sierpinski triangle, however they will converge on the triangle. If**v**_{1}is outside the triangle, the only way**v**_{n}will land on the actual triangle, is if**v**_{n}is on what would be part of the triangle, if the triangle was infinitely large.**Or more simply:**- Take 3 points in a plane to form a triangle, you need not draw it.
- Randomly select any point inside the triangle and consider that your current position.
- Randomly select any one of the 3 vertex points.
- Move half the distance from your current position to the selected vertex.
- Plot the current position.
- Repeat from step 3.

*Note: This method is also called the Chaos game. You can start from any point outside or inside the triangle, and it would eventually form the Sierpinski Gasket with a few leftover points. It is interesting to do this with pencil and paper. A brief outline is formed after placing approximately one hundred points, and detail begins to appear after a few hundred.***Or using an Iterated function system**An alternative way of computing the Sierpinski triangle uses an Iterated function system and starts by a point at the origin (*x*_{0}= 0,*y*_{0}= 0). The new points are iteratively computed by randomly applying (with equal probability) one of the following three coordinate transformations (using the so called chaos game):*x*_{n+1}= 0.5*x*_{n}*y*_{n+1}= 0.5*y*_{n}; a half-size copy

This coordinate transformation is drawn in yellow in the figure.*x*_{n+1}= 0.5*x*_{n}+ 0.25*y*_{n+1}= 0.5*y*_{n}+ 0.5 ; a half-size copy shifted right and up

This coordinate transformation is drawn using red color in the figure.*x*_{n+1}= 0.5*x*_{n}+ 0.5*y*_{n+1}= 0.5*y*_{n}; a half-size copy doubled shifted to the right

When this coordinate transformation is used, the triangle is drawn in blue.**Or using an L-system**— The Sierpinski triangle drawn using an L-system.**bitwise AND**- The 2D AND function, z=AND(x,y) can also produce a white on black right angled Sierpinski triangle if all pixels of which z=0 are white, and all other values of z are black.**bitwise XOR**- The values of the discrete, 2D XOR function, z=XOR(x,y) also exhibit structures related to the Sierpinski triangle. For example, one could generate the Sierpinski triangle by setting up a 2 dimensional matrix, [rows][columns] placing the uppermost point on [1][n/2], then cycling through the remaining cells row by row the value of the cell being XOR([i-1][j-1],[i-1][j+1])**Other means**— The Sierpinski triangle also appears in certain cellular automata (such as Rule 90), including those relating to Conway's Game of Life. The automaton "12/1" when applied to a single cell will generate four approximations of the Sierpinski triangle.## [edit] Properties

The Sierpinski triangle has Hausdorff dimension log(3)/log(2) ≈ 1.585, which follows from the fact that it is a union of three copies of itself, each scaled by a factor of 1/2.If one takes Pascal's triangle with 2^{n}rows and colors the even numbers white, and the odd numbers black, the result is an approximation to the Sierpinski triangle. More precisely, the limit as*n*approaches infinity of this parity-colored 2^{n}-row Pascal triangle is the Sierpinski triangle.The area of a Sierpinski triangle is zero (in Lebesgue measure). The area remaining after each iteration is clearly 3/4 of the area from the previous iteration, and an infinite number of iterations results in zero. Intuitively one can see this applies to any geometrical construction with an infinite number of iterations, each of which decreases the size by an amount proportional to a previous iteration.^{[citation needed]}## [edit] Analogues in higher dimensions

The tetrix is the three-dimensional analogue of the Sierpinski triangle, formed by repeatedly shrinking a regular tetrahedron to one half its original height, putting together four copies of this tetrahedron with corners touching, and then repeating the process. This can also be done with a square pyramid and five copies instead. A tetrix constructed from an initial tetrahedron of side-length L has the property that the total surface area remains constant with each iteration.The initial surface area of the (iteration-0) tetrahedron of side-length L is . At the next iteration, the side-length is halvedand there are 4 such smaller tetrahedra. Therefore, the total surface area after the first iteration is:This remains the case after each iteration. Though the surface area of each subsequent tetrahedron is 1/4 that of the tetrahedron in the previous iteration, there are 4 times as many—thus maintaining a constant total surface area.The total enclosed volume, however, is geometrically decreasing (factor of 0.5) with each iteration and asymptotically approaches 0 as the number of iterations increases. In fact, it can be shown that, while having fixed area, it has no 3-dimensional character. The Hausdorff dimension of such a construction is which agrees with the finite area of the figure. (A Hausdorff dimension between 2 and 3 would indicate 0 volume and infinite area.)## [edit] See also

*“I am not a physicist, BUT, I read a Wiki article about Sierpinski triangle. This is a model for self-organizing systems like, flocks of birds. Any single bird only gets its cues from its immediate neighbours and that is how the flock organizes itself. The clue was that they describe these particles as flocks but it should be no surprise, (no surprise at all) that these particles are self-organizing systems. If they weren't we wouldn't be here and nothing else would be here either. Nothing at all.”*See Inside## Particles That Flock: Strange Synchronization Behavior at the Large Hadron Collider

Scientists at the Large Hadron Collider are trying to solve a puzzle of their own making: why particles sometimes fly in sync

Friday, February 11, 2011 | 33

Image: Copyright CERn, for the benefit of the CMS Collaboration

In its first six months of operation, the Large Hadron Collider near Geneva has yet to find the Higgs boson, solve the mystery of dark matter or discover hidden dimensions of spacetime. It has, however, uncovered a tantalizing puzzle, one that scientists will take up again when the collider restarts in February following a holiday break. Last summer physicists noticed that some of the particles created by their proton collisions appeared to be synchronizing their flight paths, like flocks of birds. The findings were so bizarre that “we’ve spent all the time since [then] convincing ourselves that what we were see ing was real,” says Guido Tonelli, a spokesperson for CMS, one of two general-purpose experiments at the LHC.The effect is subtle. When proton collisions result in the release of more than 110 new particles, the scientists found, the emerging particles seem to fly in the same direction. The high-energy collisions of protons in the LHC may be uncovering “a new deep internal structure of the initial protons,” says Frank Wilczek of the Massachusetts Institute of Technology, winner of a Nobel Prize for his explanation of the action of gluons. Or the particles may have more interconnections than scientists had realized. “At these higher energies [of the LHC], one is taking a snapshot of the proton with higher spatial and time resolution than ever before,” Wilczek says.When seen with such high resolution, protons, according to a theory developed by Wilczek and his colleagues, consist of a dense medium of gluons—massless particles that act inside the protons and neutrons, controlling the behavior of quarks, the constituents of all protons and neutrons. “It is not implausible,” Wilczek says, “that the gluons in that medium interact and are correlated with one another, and these interactions are passed on to the new particles.”If confirmed by other LHC physicists, the phenomenon would be a fascinating new finding about one of the most common particles in our universe and one scientists thought they understood well.### 33 Comments

Add CommentShow All | Jump To: 1-10 | 11-20 | 21-30 | 31-40 | NextView- 1. BillionsNbillions 09:50 AM 2/11/11
- This synchronization seems to indicate some sort of entanglement. There may be no limit up or down on the size or mass of particles that can be entangled.Reply | Report Abuse | Link to this

- 2. AbsoluteBeginner 10:31 AM 2/11/11
- I am not a physicist, BUT, I read a Wiki article about Sierpinski triangle. This is a model for self-organizing systems like, flocks of birds. Any single bird only gets its cues from its immediate neighbours and that is how the flock organizes itself. The clue was that they describe these particles as flocks but it should be no surprise, (no surprise at all) that these particles are self-organizing systems. If they weren't we wouldn't be here and nothing else would be here either. Nothing at all.Reply | Report Abuse | Link to this

- 3. jtdwyer 10:37 AM 2/11/11
- Instead of simply referring to the high resolution images indicating these effects, a video would have been worth a million words!Reply | Report Abuse | Link to this

This is very interesting, but unfortunately there's not nearly enough information here to make any assessment. I'm certainly no expert but, of course, I'll guess anyway.

Since the LHC is colliding beams of protons, they should principally disintegrate into quarks and gluons. As I understand, gluons are, in standard theory, the mediators of the strong nuclear force that binds protons and neutrons together.

The strong force is the strongest force known, but its effective range is exceedingly limited. However, its effectiveness may well diminish gradually (perhaps in accordance with (some quantum variation of) the law of inverse-squares). In that case, the protons' directional momentum at impact is likely also imparted to the component quarks and other residue, and the 'gradually' disintegrating strong nuclear force that had bound them together.

As I understand, the allocation of mass quantities to specific types of Fermion particles (matter) is based on averages of the observed distances they traverse prior to their decay. Using increasing velocities in collider experiments has produced three 'generations' of Fermions with increasing mass assignments. It seems to me that these more energetic particles may simply indicate an increasing amount of momentum imparted to the collision byproducts, producing increased distances traversed prior to decay. In this view, aren't the more massive generations of Fermions simply artifacts of the velocity imparted to test collisions?

At any rate, this 'interaction of gluons' affecting particle trajectories may simply the gradual diminishment of the strong force as distance increases, analogous to the diminishing effects of gravitation...

- 4. rajnish 11:16 AM 2/11/11
- Entanglement and relativity are independent of direction of motion in free space. In fact the former one is independent of distance and the later one is dependent on magnitude of velocity. Time is nothing and in particular present time represents degree of synchronization of an observer with other things. These kind of observations only point out that we have to search at far down level to know the reality or settle for the concept of free will.Reply | Report Abuse | Link to this

- 5. batmanroxus 12:22 PM 2/11/11
- Here is the Higgs and the model that defines dark matter, dark energy and simplifies black holes. This theory very effectively replaces big bang and simplifies everything. The Higgs particle is not tiny, it's HUGE. waynemcmichael [dot] com [slash] iwtReply | Report Abuse | Link to this

- 6. rloldershaw 12:57 PM 2/11/11
- Reply | Report Abuse | Link to this

Here is the most important message.

Beyond the heuristic Standard Model of particle physics that has been in place for decades, none of the new pseudo-physics offered by our heroic theorists [SUSY "sparticles", "Higgs boson", "extra dimensions", and most importantly any form of "particle dark matter"] have showed up. We're on a fool's errand that has been going on for at least a decade.

What does that tell you?

I'd say time for new ideas from a new segment of the scientific community, with emphasis on nonlinear dynamical systems, fractals, deterministic chaos and other real-world physics available since Poincare discovered that the Solar System was not exactly integrable and that perfectly "reversible" systems were a Platonic ideal.

Real-world systems are fully causal, deterministic, dissipative and irreversible. If the math says otherwise, it is because its starting assumptions are way over-idealized. Let's get back to reality.

RLO

www.amherst.edu/~rloldershaw

- 7. batmanroxus 01:11 PM 2/11/11
- I second what rlodershaw said:) It's like and easter egg hunt in a cow pasture... You have to watch out for the BS:)Reply | Report Abuse | Link to this

- 8. gesimsek 03:43 PM 2/11/11
- Why can't the gluons glue the atom of radiactive elements? What glues the non-particle matrix of space-time?Reply | Report Abuse | Link to this

- 9. jtdwyer 04:38 PM 2/11/11
- I do wonder whether the gluons represent the interaction between quarks (material energy) and a confining external field of potential energy (mass), reconfigured from the kinetic energy of initial wave emission.Reply | Report Abuse | Link to this

I suspect that the matrix of spacetime coordinates represents the distribution of residual kinetic energy (and the dimensions of space and time that its disbursal produces) released during the origination of the universe.

- 10. jtdwyer 04:42 PM 2/11/11
- I strongly empathize with your sentiments, but in my opinion it is the reliance on analytical models to functionally represent physical/mechanical systems that has produced the evidentiary disconnect between physics and reality. I don't think that any new reliance on some deeper level of analytic mathematical abstraction can provide a more direct correspondence with physical reality.Reply | Report Abuse | Link to this

- 11. bob94561 05:25 PM 2/11/11
- I have followed the progress of the hadron collider for some time. I find it very interesting to hear about their new findings. I hope that one day they will collide Antimatter particles together. I'm wondering it that will open a true black hole? Maybe even time it's self. Thanks for all your hard work. keep it up.Reply | Report Abuse | Link to this