Check out these photos of fractals in nature:

Although the fractal above was generated purely by a mathematical formula, it bears a striking resemblance to the deity known as Sri Ganesh - in fact if one looks more closely, one can see a number of likenesses of Sri Ganesh's face, complete with ornaments and crown. The overall shape also looks like a person sitting cross-legged, meditating. Some people may view this likeness as a pure coincidence, but if one considers that the formula which generates the image is relatively simple, and it was not "fiddled" to improve the image in any way, it seems like more than just a "coincidence".
Indeed the mathematician who first discovered the image remarked: "If I were a religious person I would certainly take this as some sort of sign".

No one disputes that the universe is far from smooth on relatively small scales - by which cosmologists mean thousands of light years. But Hogg's team is convinced that if you zoom further out, smoothness reigns. "When you're looking at the size scales of galaxies, groups of galaxies, clusters, superclusters and filaments, it looks like a fractal," says Hogg. "But once you get larger than all of that, then it starts to look homogeneous."What has convinced him is his team's analysis of the latest data from the Sloan Digital Sky Survey, the largest 3D map of the galactic universe so far. His team insists that the map is proof of smoothness. The fractal camp, however, are sceptical. In fact, they say the Sloan observations confirm what they've been claiming all along. It might appear to be deadlock, but at least with the Sloan survey the two sides can agree what they're disagreeing about. For years Pietronero and his team argued that the statistical methods mainstream cosmologists were using to establish homogeneity were flawed because they start off by assuming that matter is evenly spread. The team was mostly ignored until 2004, when Hogg and astrophysicist Daniel Eisenstein of the University of Arizona in Tucson spent a summer in Paris with Pietronero's colleagues, cosmologists Francesco Sylos Labini of the Enrico Fermi Centre and the Institute for Complex Systems, Rome, and Michael Joyce of the Pierre and Marie Curie University, Paris. "We argued every day about fractals," Hogg says. "Those battles raged over lunch and coffee and finallyconvinced us by the end of our visit that we should be doing the analysis as they say."When they returned to the US, Hogg and Eisenstein applied the fractal team's methods to a sample of 55,000 luminous red galaxies mapped by Sloan. They found that the galaxies do form a fractal pattern, but as they looked at bigger and bigger scales, the pattern appeared to disintegrate and smooth out at just over 200 million light years - a scale far larger than most cosmologists had expected.But Pietronero and Sylos Labini are not convinced. Instead, they believe that if astronomers could continue to zoom out and look at even larger scales, they would find more clustering. They suspect that the apparent smoothness at 200 million light years is not real, but rather an illusion created by statistical effects due to the limited range of the Sloan survey. Hogg's team, though, insist that their evidence of homogeneity is statistically significant. "I think the result really is secure," says Hogg. "I would stake my scientific reputation on that."Even if the result is real, mainstream cosmologists still have a huge problem on their hands. The fact that the fractal patterning extends to far bigger scales than anyone had expected means that there must be far bigger structures than anyone expected - structures that are even bigger than superclusters. The fractal team argues that the standard model cannot explain the existence of these galactic giants. "If you look at the galaxy data, you can see enormous objects hundreds of millions of light years across, stuff that's really huge," says Pietronero. "This is a huge problem. You're going to have to change the story very radically." The usual story runs something like this. In the tiny fluctuations of the nascent universe, matter began to collect in denser regions, setting off a chain reaction of gravitational collapse that has given us the large-scale structure we see today. Gravity has worked from the bottom up, building galaxies first, then collecting galaxies into clusters, then clusters into superclusters and so forth. But while the matter has been clumping together, the universe has been expanding, and thus a battle has ensued: gravity versus expansion. According to Pietronero, there simply hasn't been enough time since the universe came into being 14 billion years ago for gravity to sculpt structures larger than about 30 million light years across: expansion would have prevented anything larger from forming. "The existence of structures much larger than this implies a crisis of the present view of structure formation," he says. This present view is the "cold dark matter model", in which the glowing masses of stars and galaxies are only the tip of the cosmic iceberg. Luminous matter makes up roughly 15 per cent of all the matter in the universe - the other 85 per cent is mysterious dark matter. Hogg's team says that the new observations do not undermine the standard view as Pietronero claims. Instead, they maintain that the cold dark matter model explains the Sloan data quite accurately. For that to betrue, however, Hogg's team have to put a number called a bias parameter into their equations. It reflects the difference between the distribution of matter in computer simulations of the cold dark matter model and the observed distribution of luminous matter. Collisions between particles of ordinary matter help it clump together, but dark matter is thought not to behave in the same way. That suggests it could be spread out in space more evenly than ordinary matter, so cosmologists assume that the distribution of the matter we can see - galaxies, say - is not a true reflection of the distribution of all the matter that is out there. They believe the structure of the universe is really much "smoother" than it appears to be, because dark matter dominates. In the case of the Sloan survey, the bias is 2: the visible galaxies are clumped twice as densely as the predicted total distribution of matter in the universe.Sylos Labini, however, sees the bias as a fudge that allows cosmologists to discount the observed clustering of galaxies and to assume that the gigantic clusters of superclusters are only half the problem they appear to be. "The bias is a way to hide the size of structures behind some ad hoc parameter," he says. Mainstream cosmologists, however, feel the bias is justified, assuming that galaxies cluster in regions of space that are replete with excess dark matter. According to the standard model, dark matter is everywhere, but galaxies only shine in the rare regions where dark matter is densest. Dark matter also lingers in the voids where no light shines but here it is thinly spread out. In other words, while the luminous galaxies look veryclustered, the underlying blanket of dark matter is far smoother, supporting the claim of homogeneity. "If the cold dark matter model is correct, then there should be dark matter in the voids," Hogg says. The million-dollar question is: what is the real distribution of dark matter? Is dark matter smooth or fractal? Is it clustered like the galaxies, or does it spread out, unseen, into the great voids? If the voids are full of dark matter, then the apparent fractal distribution of luminous matter becomes rather insignificant. But if the voids are truly empty, the fractal claim requires a closer look. Astronomers are now providing our first glimpse into the voids and our first look at the pattern of invisible matter. Richard Massey of the California Institute of Technology in Pasadena and others in the Cosmic Evolution Survey project have just created the first 3D map of dark matter in the universe (New Scientist, 13 January, p 5). They were able to find the dark matter by observing its gravitational effect on any light streaming past it. Combining data from the Hubble Space Telescope, the Subaru telescope in Hawaii and the Very Large Telescope in Chile, they mapped the distribution of dark matter at scales ranging from 23 million to 200 million light years across. Massey's team found that the dark matter distribution is nearly identical to the luminous matter distribution. "The first thing that strikes me is the voids," Massey says. "Vast expanses of space are completely empty. The dark matter makes up a criss-crossing network of strings and sheets around these voids. And all the luminous matter lies within the densest regions of dark matter."Although this distribution of dark matter seems to favour the idea that the universe is fractal, Hogg isn't convinced. "It is interesting," he says, "but measurements of dark matter are much less precise than measurements of galaxy distributions.""The result is very new," Massey agrees. "It demonstrates a very exciting new way of looking directly at dark matter and will be vital in future work, but hasn't yet been subject to all the analysis that has been applied to galaxy surveys." When asked if the dark matter exhibits an explicitly fractal structure, Massey replies, "We don't know yet." "The universe is not a fractal," Hogg insists, "and if it were a fractal it would create many more problems that we currently have." A universe patterned by fractals would throw all of cosmology out the window. Einstein's cosmic equations would be tossed first, with the big bang and the expansion of the universe following closelybehind. Hogg's team feel that until there's a theory to explain why the galaxy clustering is fractal, there's no point intaking it seriously. "My view is that there's no reason to even contemplate a fractal structure for the universe until there is a physical fractal model," says Hogg. "Until there's an inhomogeneous fractal model to test, it's like tilting at windmills."Pietronero is equally insistent. "This is fact," he says. "It's not a theory." He says he is interested only in what he sees in the data and argues that the galaxies are fractal regardless of whether someone can explain why. As it turns out, there is one model that may be able to explain a fractal universe. The work of a little-known French astrophysicist named Laurent Nottale, the theory is called "scale relativity" (see "Fractured space-time"). According to Nottale, the distribution of matter in the universe is fractal because space-time itself is fractal. It is a theory on the fringe, but if the universe does turn out to be fractal, more people might sit up and take notice. A resolution to the fractal debate will only come with more data. Sloan is currently charting more galaxies andwill release a new map in the middle of 2008. According to Sylos Labini, this will cover over 650 million light years and should tell us if the apparent transition to homogeneity extends beyond 200 million light years. For now, the pattern of the world, imprinted at the origin of the universe, remains a secret glimpsed only in the knowing shimmer of the stars."

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