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There are many different types of fractals.
first well-known Fractal feel is still very popular genre today. This is the famous Mandelbrot set. Relatively simple algorithm that is used to make it, was presented to the public in 1985 by Scientific American magazine. A lot of the first pictures came from Fractal Mandelbrot set (or Julia overnight), including many beautiful spiral shapes.
However, there are many other types of fractals. One particularly beautiful fractal type is “3D Strange attractors cell” (sometimes called “flame Fractal”) that maps the paths points to certain contacts … this Fractal produces images which can look something like smoke, fire, patterns of reflected light even flowers and feathers.
Other types Fractal is IFS Fractal that can produce beautiful patterns in places that gradually fill the “zoom pollution” (as Fractal Zoom record is shaping all Fractal would fill if given infinite time). The IFS Fractal is also the basis of the well know JPEG image compression format.
All of the above fractal types can be generated easily using open source software, and are incredibly fascinating to explore for you.
A lot of abstract art, in particular “organic abstract” art, is fractal in nature. Also, labels made of watercolor paper, or oil on canvas, fractal in nature, what the signals are used to represent.
Nature itself is also mainly Fractal … plant orbits, Galaxy form, sunspots, plant and tree form, sound, waterfall, waves, the sound of the wind, the patterns of shells, and most of the rest of nature, all built of different fractals.
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