Researchers develop three-step process for building fractal nanostructures

Researchers develop three-step process for building fractal nanostructures: Greer's group has developed a three-step process for building such complex structures very precisely. They first use a direct laser writing method called two-photon lithography to "write" a three-dimensional pattern in a polymer, allowing a laser beam to crosslink and harden the polymer wherever it is focused. At the end of the patterning step, the parts of the polymer that were exposed to the laser remain intact while the rest is dissolved away, revealing a three-dimensional scaffold. Next, the scientists coat the polymer scaffold with a continuous, very thin layer of a material—it can be a ceramic, metal, metallic glass, semiconductor, "just about anything," Greer says. In this case, they used alumina, or aluminum oxide, which is a brittle ceramic, to coat the scaffold. In the final step they etch out the polymer from within the structure, leaving a hollow architecture.

Sun's fractal surprise could help fusion on Earth - space - 01 May 2014 - New Scientist

Sun's fractal surprise could help fusion on Earth - space - 01 May 2014 - New Scientist: STEREO revealed that when the movement of the wind's particles is perpendicular to the sun's magnetic field, they resemble a fluid, with sections that are smooth, interrupted by bursts of violence...

But when the particles move in parallel with the field lines, they behave very differently, with the turbulence evenly spread, like crinkly mountains that extend as far as the eye can see...

One problem with optimising their energy output is deducing what is going on inside them – inserting a probe isn't an option as it would melt...

By adding the fractal behaviour to their plasma models, fusion scientists may be able to control turbulence, which can cause plasma to escape the magnetic field containing it in the reactor...

Turbulent black holes grow fractal skins as they feed - physics-math - 28 April 2014 - New Scientist

Turbulent black holes grow fractal skins as they feed - physics-math - 28 April 2014 - New Scientist: "We showed that when you throw stuff into a black hole, the surface of the black hole responds like a fluid – and in particular, it can become turbulent...  More precisely, the horizon itself becomes a fractal..."

To investigate what the horizon of a black hole looks like at mealtime, Adams took advantage of a mathematical duality between Einstein's equations of general relativity – which describe gravity near black holes – and fluid dynamics...

Led by Paul Chesler, who is a post-doc researcher at Harvard, the team first modelled a turbulent fluid system. They then translated it into the black hole regime and let it develop with time. When they looked again, the horizon of the black hole appeared to have developed an infinite surface area.

Physicists Net Fractal Butterfly: Scientific American

Physicists Net Fractal Butterfly: Scientific American: ...the pattern describes the behavior of electrons in extreme magnetic fields...

...It was known at the time that electrons under the influence of a magnetic field would race around in circles. But Hofstadter found that in theory, if the electrons were confined inside a crystalline atomic lattice, their motion would become complicated. As the magnetic field was cranked up, the energy levels that define the motion of electrons would split again and again. When represented on a graph, those energy levels revealed a pattern that looked like a butterfly — and continued to do so, even when zoomed in to infinitely small scales...

 In May, researchers reported that they had stacked a single sheet of graphene, in which carbon atoms are arranged like a honeycomb, on top of a sheet of honeycombed boron nitride. The layers create a repeating pattern that provides a larger target for magnetic fields than the hexagons in each material — effectively magnifying the field.

Team uses fractal geometry to build lighter structures

Team uses fractal geometry to build lighter structures: The first step is to create a hollow metal beam of the size desired for a given project. Next, reengineer the beam by changing its diameter and thickness such that the beam weighs as little as possible but is still able to withstand the weight or pressure it will be subjected to as a final structure. Once that is achieved, label it generation-0. The next step is to create a larger beam made out of generation-0 beams arranged using triangular subdivisions. This next beam is labeled a generation-1 beam...

...the researchers suggest that a solar sail made with a solid metal 100 meter boom (not that anyone is proposing that) could be made to be 10,000 times lighter if a generation-3 beam were used instead.

Giant fractals are out – the universe is a big smoothie - New Scientist - New Scientist

Giant fractals are out - the universe is a big smoothie: They tested for clusters by placing any given galaxy in the centre of an imaginary sphere and counted the number of galaxies within it. If clustering exists, there should be more galaxies within a sphere than if the 220,000 galaxies were distributed randomly throughout the huge cube.

With relatively small spheres – up to about 330 million light years wide – they did find galactic clusters. But in larger spheres the number of galaxies met expectations for randomness.

Mathematicians develop new method for describing extremely complicated shapes

Mathematicians develop new method for describing extremely complicated shapes:Bridging the topology and fractals, as described in the American Institute of Physics' Journal of Mathematical Physics (JMP), relies upon a recently developed mathematical theory, known as "persistent homology," which takes into account the sizes and number of holes in a geometric shape. The work described in JMP is a proof of concept based on fractals that have already been studied by other methods – such as the shapes assumed by large polymer molecules as they twist or bend under random thermal fluctuation.

Superconductivity associated with fractal structure of nanoscale electron lines

Superconductivity associated with fractal structure of nanoscale electron lines:  Said Dahmen, “We decided to make histograms of the sizes of these regions and compare them with predictions from various models. We found they agreed with those from models that also had fingery regions in the bulk of the material—the agreement was striking.”

Carlson explained, “We noticed that the pattern of orientations of the nanoscale lines doesn’t depend on the scale of the image. The pattern looks the same whether we view the entire image, or whether we view smaller and smaller pieces of it—the pattern is fractal.

“Every fractal has its own set of characteristic numbers, as unique as a fingerprint. You might imagine that the characteristic numbers for a fractal which is happening only on the surface would be different from the characteristic numbers for a fractal which really originates from deep inside the material.

“When we studied the characteristic numbers of this fractal, we discovered telltale signs in its fingerprint that indicate this is not just a surface fractal.  Rather, it is coming from deep inside the material. We are seeing a 3-D fractal, which then intersects the surface of the material.”

Pharaoh's playground revealed by missing fractals

Pharaoh's playground revealed by missing fractals: Ramisch and his team generated a digital model of the topography around Dahshur and assessed its fractal geometry as part of their archaeological investigations. They found a surprisingly large area around the pyramids - at least 6 square kilometres - where the natural fractal geometry was absent. The find suggests that the entire area was once modified...
The disturbance to the natural fractals can even give a sense of what occupied the site. In this case, says Ramisch, it was probably broad terraces several kilometres long, which would have "increased the sense of monumentality of the pyramids".

BBC News - Subways 'share universal structure', research suggests

BBC News - Subways 'share universal structure', research suggests: In some senses, it is unsurprising that the study found that networks tended over time to comprise a dense core of central stations with a number of lines radiating outward from it...

But the analysis shows a number of less obvious similarities across all 14 networks.
It found the total number of stations was proportional to the square of the number of lines - that is, a four-fold increase in station number would result in a doubling of the number of lines.
The dense core of central stations all had the same average number of neighbours in the network, and in all cases, about half the total number of stations were found outside the core.
In addition, the length of any one branch from the core's centre was about the same as twice the diameter of the core.
The number of stations at a given distance from the centre was proportional to the square of that distance, but only up to the edge of the core; at more distant reaches of the network, the number of stations contained was directly proportional to distance...
The authors say that the systems do not appear to be "fractal".

The Bizarre Object We Believed Was Impossible to Visualize

The Bizarre Object We Believed Was Impossible to Visualize: Is it possible to visualize this object in 3-D space? You might not think so — after all, a globe cannot be flattened into two dimensions, without distorting the distance between points on it. However, researchers in France have now accomplished exactly that.

The key, they explain, is to use corrugations. They piled up corrugations, until the distances between points was accurate.

The resulting surfaces of the objects are what are known as smooth fractals, which the researchers say lie halfway between fractals and ordinary surfaces...

'Infinity Computer' Calculates Area Of Sierpinski Carpet Exactly - Technology Review

'Infinity Computer' Calculates Area Of Sierpinski Carpet Exactly - Technology Review  Sergeyev begins by adding a new axiom to the axiom of real numbers, which he calls the infinite unit axiom. This introduces grossone--the infinite unit.

Because it is governed by the other axioms of real numbers, grossone behaves much like one too. So it's possible to multiply grossone, divide it, add to it and subtract from it, just as is possible with other real numbers.

That suddenly makes working at infinity much easier by using a computing process that Sergeyev calls the infinity computer, which has the additional axiom built in. "The introduction of grossone gives a possibility to work with finite, infinite and infinitesimal quantities numerically," he says.

To show off its power, he works through the Sierpinski carpet examples given above, revealing how it's possible to keep track of the number of iterations at infinity simply by adding or subtracting real numbers from grossone. If a square can created in grossone steps, a square doughnut can be created in -grossone minus 1- steps. In this way, it's a simple matter to differentiate between any of the shapes in carpet sequence.

Tiny fractal trees for solar power

Tiny fractal trees for solar power: In this case, branches of silver 1-50th the width of a human hair are themselves branched, and smaller branches grow on those branches, forming a treelike pattern.
In a solar cell application, the silver trees are coated with light-absorbing polymers. When light particles (photons) hit the polymer coat, they produce short-lived electrons and holes in the polymer.

The beat goes on: the geometry that makes music pleasing | Faculty of Science - McGill University

The beat goes on: the geometry that makes music pleasing | Faculty of Science - McGill University: The researchers found that all the musical compositions they studied shared the same "fractal" quality, where the part is a more limited repetition of the whole. That is the larger temporal structure of well-formed musical pieces is composed of repeating motifs of their own short-term temporal structure.  At the same time, researchers also discovered that each composer had his or her own highly individual rhythmic signature. “This was one of the most unanticipated and exciting findings of our research,” asserts Levitin. “Mozart's notated rhythms were the least predictable, Beethoven's were the most, and Monteverdi and Joplin had nearly identical, overlapping rhythm distributions. But they each have their own distinctive rhythmic signature that you can capture.

Alexander's Horned Sphere fractal changes how we define inside and outside

Alexander's Horned Sphere fractal changes how we define inside and outside: Other fractals occupy decimal dimensions or are seemingly solid shapes that are actually all surface area - this fractal can divide the world into one single spherical 'inside' but more than one 'outside.'

Getting just a little crazier, this is only even conceptually possible in a three dimensional universe. The Jordan Curve Theorem, showed that there is no single, enclosed curve that cannot carve a two-dimensional plane into an inside and an outside that mirror each other. It's only in the universe that we perceive that things can get more complicated than that. It's only in our reality that one spherical inside creating more than one outsides is possible.

Scientists still puzzled by a fractal discovered 500 years ago

Scientists still puzzled by a fractal discovered 500 years ago: Strip the leaves off of the average tree, soak the whole thing in water until it gets mushy, bundle the branches up together, and you'll get what looks like one long trunk. That's what Leonardo Da Vinci said in the fifteen hundreds. If a tree trunk splits off into three main branches, each of the branches will be one third the size of the trunk. When each of those branches splits into three again, making nine branches on the second 'tier' of the tree, each of these second tier branches will be one ninth the side of the trunk. As the branches grow and split, they will always be a particular fraction of the size of the trunk, and adding together all the fractional bits of each 'tier' of branches will always add up to 'one trunk.'

Soot coating creates self-cleaning surface

Soot coating creates self-cleaning surface: A candle flame will coat a glass slide with black soot. The soot looks uniform, but a scanning electron microscope reveals a fractal-like network of carbon particles that makes it superhydrophobic, or incredibly water-repellent...
Now, researchers at the Max Planck Institute for Polymer Research in Mainz, Germany, and the Technical University Darmstadt, also in Germany, have realised that coating the soot particles in a thin layer of silica replicates their water-repelling structure. They then heat the surface to 600 °C for 2 hours to destroy the soot particles, leaving behind the see-through silica.

Role of fractal dimension in random walks on scale-free networks

Role of fractal dimension in random walks on scale-free networks: Fractal dimension is central to understanding dynamical processes occurring on networks; however, the relation between fractal dimension and random walks on fractal scale-free networks has been rarely addressed, despite the fact that such networks are ubiquitous in real-life world. In this paper, we study the trapping problem on two families of networks.

Scientists use fractals to determine when bananas are becoming mushy and inedible

Scientists use fractals to determine when bananas are becoming mushy and inedible: Bananas (Musa cavendish) were stored for 10 days at 20 �C. and scans of the banana surfaces were recorded using a computational vision system. The team worked on the basis that the banana spots can, to some extent, reflect changes in the ripening process – and that the daily increase in spots might, to some extent, follow a fractal pattern.

The Menger Sponge literally straddles the line between different dimensions

The Menger Sponge literally straddles the line between different dimensions: A particular fractal, called Menger's Sponge, is all about surface appearances. It's a purely theoretical shape that has infinite surface area and no volume whatsoever. And because of that, it doesn't occupy three dimensions. Or two. It manages to exist in fractional dimensions...

the Sierpinski Carpet is supposed to have a fractional dimension of 1.89, and the Menger Sponge, which has no real volume, has a fractional dimension of 2.73.