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Asset ID: 102491873 / Petra Stefankova / A colorful image of two angels floating on clouds
The Mandelbrot set is a particular mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoît Mandelbrot , who studied and popularized it.
More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial z n +1 = z n 2 + c remains bounded . That is, a complex number c is part of the Mandelbrot set if, when starting with z 0 = 0 and applying the iteration repeatedly, the absolute value of z n remains bounded however large n gets.
For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is defined as i 2 = −1 ) gives the sequence 0, i , (−1 + i ), −i , (−1 + i ), −i , ..., which is bounded, and so i belongs to the Mandelbrot set.
Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.
The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization .
<div id="index_ignore">Description above from the Wikipedia article Mandelbrot set, licensed under CC-BY-SA full list of contributors here. This page is not affiliated with, or endorsed by, anyone associated with the topic.</div>
The Mandelbrot set is a particular mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoît Mandelbrot , who studied and popularized it.
More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial z n +1 = z n 2 + c remains bounded . That is, a complex number c is part of the Mandelbrot set if, when starting with z 0 = 0 and applying the iteration repeatedly, the absolute value of z n remains bounded however large n gets.
For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is defined as i 2 = −1 ) gives the sequence 0, i , (−1 + i ), −i , (−1 + i ), −i , ..., which is bounded, and so i belongs to the Mandelbrot set.
Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.
The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization .
<div id="index_ignore">Description above from the Wikipedia article Mandelbrot set, licensed under CC-BY-SA full list of contributors here. This page is not affiliated with, or endorsed by, anyone associated with the topic.</div>
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Keep your favorite image, design, or words of inspiration close your heart with this beautiful square custom sterling silver plated necklace. Complete with a 18" sterling silver-plated chain (2" extender) and lobster claw clasp, this necklace is finished with a UV resistant and waterproof coating to protect your imagery for years to come. The necklace arrives in a special black felt bag that is perfect for gifting.
- Sterling Silver-Plate.
- Made in the USA.
- UV Resistant and waterproof.
- Add photos, artwork and text.
- Charm diameter: 1.38".
- Chain length: 18" with 2" extender.
Found in the A colorful image of two angels floating on shop category at Zazzle, the amazing "dithered colour" necklace design above was contributed by a very skilled designer named prophoto. Given the title, “a colorful image of two angels floating on necklace”, this particular custom necklace is just a minute fraction of the countless fabulous necklace designs that are available for sale online in the Zazzle community marketplace. While the creator appropriately dubbed this customizable necklace charm as the “a colorful image of two angels floating on necklace”, you'll be able to find other similar merchandise if you search for the tags, togetherness, fantasy, bizarre, or humor. You will most certainly find an ideal necklace charm design very quickly.
Created using our technologically-advanced custom pendant printing process, this custom necklace will look stunning with prophoto’s fantasy illustration. With an ideal surface for printing, this Zazzle custom necklace charm is a great way to dress up any outfit. Select the necklace displayed above, or try looking for other A colorful image of two angels floating on items in the marketplace. Regardless of when you decide to wear it, this custom necklace charm will look amazing and it will undoubtedly make this seller's design a delightful togetherness addition to anyone's collection of pendants.
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A colorful image of two angels floating on
Asset ID: 102491873 / Petra Stefankova / A colorful image of two angels floating on clouds
The Mandelbrot set is a particular mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoît Mandelbrot , who studied and popularized it.
More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial z n +1 = z n 2 + c remains bounded . That is, a complex number c is part of the Mandelbrot set if, when starting with z 0 = 0 and applying the iteration repeatedly, the absolute value of z n remains bounded however large n gets.
For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is defined as i 2 = −1 ) gives the sequence 0, i , (−1 + i ), −i , (−1 + i ), −i , ..., which is bounded, and so i belongs to the Mandelbrot set.
Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.
The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization .
The Mandelbrot set is a particular mathematical set of points whose boundary is a distinctive and easily recognizable two-dimensional fractal shape. The set is closely related to Julia sets (which include similarly complex shapes), and is named after the mathematician Benoît Mandelbrot , who studied and popularized it.
More precisely, the Mandelbrot set is the set of values of c in the complex plane for which the orbit of 0 under iteration of the complex quadratic polynomial z n +1 = z n 2 + c remains bounded . That is, a complex number c is part of the Mandelbrot set if, when starting with z 0 = 0 and applying the iteration repeatedly, the absolute value of z n remains bounded however large n gets.
For example, letting c = 1 gives the sequence 0, 1, 2, 5, 26,…, which tends to infinity. As this sequence is unbounded, 1 is not an element of the Mandelbrot set. On the other hand, c = i (where i is defined as i 2 = −1 ) gives the sequence 0, i , (−1 + i ), −i , (−1 + i ), −i , ..., which is bounded, and so i belongs to the Mandelbrot set.
Images of the Mandelbrot set display an elaborate boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts.
The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules, and is one of the best-known examples of mathematical visualization .
Description above from the Wikipedia article Mandelbrot set, licensed under CC-BY-SA full list of contributors here. This page is not affiliated with, or endorsed by, anyone associated with the topic.
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Product id: 177479265534085902Made on 2/14/2012 3:53 PM
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