Free Republic

Explanation: What strange world is this? Pictured above is no real place but rather a purely mathematical visualization of a generalization of a fractal into three dimensions. Classical fractal diagrams are typically confined to the two dimensions inherent in the complex number plane, demarking regions where an iterative function diverges. Recently explored additions expand the Mandelbrot set of fractals to three dimensions with prescriptions dubbed Mandelbox and Mandelbulb sets. The results are often visually stunning creations of virtual worlds with limitless detail, some of which you can fly through. Pictured above is one such mathematical fantasy, possibly reminiscent of some...

The Dahshur royal necropolis in Egypt was once a dazzling sight. Some 30 kilometres south of Cairo, it provided King Sneferu with a playground to hone his pyramid-building skills - expertise that helped his son, Khufu, build the Great Pyramid of Giza. But most signs of what went on around Dahshur have been wiped away by 4500 years of neglect and decay. To help work out what has been lost, archaeologists have turned to fractals. All around the world, river networks carve fractal patterns in the land that persist long after the rivers have moved on (see picture). "You can...

Is there a better way to do the people’s business in commerce, legislation, education, bureaucracy and even religion in a Constitutional Republic? Is chaos only violent disorder? The weather and climate change naturally operate on Chaos Theory. Chaos is not disorder unless it goads the ignorant into rioting in the streets, usually burning and pillaging the visions and labor of others. In human discourse, the beautiful freely formed fractals of natural chaos makes a free society work by creating infinite beauty, opportunities for new relationships, ideas, ventures and true diversity based on our individual endowments from God. Chaos Theory views...

Benoit B. Mandelbrot, a maverick mathematician who developed an innovative theory of roughness and applied it to physics, biology, finance and many other fields, died on Thursday in Cambridge, Mass. He was 85. His death, at a hospice, was caused by pancreatic cancer, his wife, Aliette, said. He had lived in Cambridge. Dr. Mandelbrot coined the term “fractal” to refer to a new class of mathematical shapes whose uneven contours could mimic the irregularities found in nature. “Applied mathematics had been concentrating for a century on phenomena which were smooth, but many things were not like that: the more you...

A Market Forecast That Says ‘Take Cover’ WITH the stock market lurching again, plenty of investors are nervous, and some are downright bearish. Then there’s Robert Prechter, the market forecaster and social theorist, who is in another league entirely. Prechter is convinced that we have entered a market decline of staggering proportions — perhaps the biggest of the last 300 years. ...... Originating in the writings of Ralph Nelson Elliott, an obscure accountant who found repetitive patterns, or “fractals,” in the stock market of the 1930s and ’40s, the theory suggests that an epic downswing is under way, Mr. Prechter...

TIMESTAMP 08/11/2009. The original Mandelbrot is an amazing object that has captured the public's imagination for 30 years with its cascading patterns and hypnotically colourful detail. It's known as a 'fractal' - a type of shape that yields (sometimes elaborate) detail forever, no matter how far you 'zoom' into it (think of the trunk of a tree sprouting branches, which in turn split off into smaller branches, which themselves yield twigs etc.). It's found by following a relatively simple math formula. But in the end, it's still only 2D and flat - there's no depth, shadows, perspective, or light sourcing....

EVER since 1996, when Pope John Paul II said that evolution (a term he did not define) was "more than just a hypothesis," defenders of neo-Darwinian dogma have often invoked the supposed acceptance - or at least acquiescence - of the Roman Catholic Church when they defend their theory as somehow compatible with Christian faith.