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From sea shells and spiral galaxies to the structure of human lungs, the patterns of chaos are all around us.
Fractals are patterns formed from chaotic equations and contain self-similar patterns of complexity increasing with magnification. If you divide a fractal pattern into parts you get a nearly identical reduced-size copy of the whole.
The mathematical beauty of fractals is that infinite complexity is formed with relatively simple equations. By iterating or repeating fractal-generating equations many times, random outputs create beautiful patterns that are unique, yet recognizable.
We have pulled together some of the most stunning natural examples we could find of fractals on our planet.
This variant form of cauliflower is the ultimate fractal vegetable. Its pattern is a natural representation of the Fibonacci or golden spiral, a logarithmic spiral where every quarter turn is farther from the origin by a factor of phi, the golden ratio.
The San Francisco Bay salt flats pictured above have been used for commercial salt production for over a century.
Extinct for 65 million years, ammonites were marine cephalopods that built chambered spiral shells. The walls between these chambers, called sutures, were complex fractal curves. Stephen Jay Gould used the complexity of ammonite sutures over time to argue that there is no evolutionary drive toward greater complexity and that we are a "glorious accident," alone in the universe
Mountains are the result of tectonic forces pushing the crust upward and erosion tearing some of that crust down. The resulting pattern is a fractal.
Above is an image of the Himalayan Mountains, home to many of the tallest peaks on Earth. The Himalayas are still being uplifted by the collision of India with the Eurasian plate, which began about 70 million years ago.
Ferns are a common example of a self-similar set, meaning that their pattern can be mathematically generated and reproduced at any magnification or reduction. The mathematical formula that describes ferns, named after Michael Barnsley, was one of the first to show that chaos is inherently unpredictable yet generally follows deterministic rules based on nonlinear iterative equations. In other words, random numbers generated over and over using Barnsley's Fern formula ultimately produce a unique fern-shaped object.
These marine stratus clouds were photographed by the Aqua satellite over the South Atlantic Ocean, off the west coast of Africa. A fractal cloud pattern is interrupted by a series of diagonal grooves. According the NASA Earth Observatory, it is highly unusual to see such a sharp boundary in a continual cloud formation such as this, and scientists have yet to explain how it could form.
The 200-mile long series of cloud vortexes is perhaps the longest of these formations ever photographed, according to NASA. These cloud vortexes are also called von Kármán cloud streets, for the late fluid dynamicist Theodore von Kármán.
Cloud streets form when low-lying clouds are interrupted by an object such as an island. Similar patterns occur in the wind flow downstream of airplane wing
Many plants follow simple recursive formulas in generating their branching shapes and leaf patterns.
This false-color image of the Grand Canyon displays the fractal pattern created by the Colorado River over millions of years. Rivers and canyons commonly form fractal patterns as tributaries merge into larger tributaries. In the above image red indicates areas of vegetation.
Peacocks attract mates with the repeating patterns in their plumage
Crystallizing water forms repeating patterns in snowflakes and on frosty surfaces. The patterns have inspired claims about the power of consciousness to affect matter, as well as one of the first described fractal curves, the Koch snowflake.
Similar to canyons, a combination of rock irregularity and gravity produces repeating patterns as water flows over the side of a sharp ledge.
The Yukon River branches into thousands of distributary channels as it drains into the Bering Sea off the coast of Alaska.
This is NOT anything to do with "chemtrails", "HAARP", "Scalar waves", nor "disinfo". If you believe they are, research it a bit, please.