Mandelbrot Set: how it is generated. Mandelbrot set - from order to chaos. Sacred Geometry. The Hardest Mandelbrot Zoom in 2016 - New record, 750 000 000 iterations! Ancient Knowledge Pt.2 Fibonacci Sequence, Golden Ratio, Phi in Nature, DNA, Fingerprint of God. Into the Mandelbrot set we go....and back out. The Thumbrint of God by Arthur C Clarke. R.I.P - Benoit Mandelbrot. "Clouds are not spheres, mountains are not cones, coastlines are not circles,and bark is not smooth,nor does lightning travel in a straight line.
"—Mandelbrot, in his introduction to The Fractal Geometry of Nature Fractals. They are one of nature's most beautiful mysteries. Benoit Mandelbrot, the French mathematician, was The Father of Fractals, for he coined the term and researched fractals as his life work. He died last week at the age of 85. The above fractal is named for him. His seminal works, Fractals: Form, Chance and Dimension and The Fractal Geometry of Nature, were published in 1977 and 1982. Benoit Mandelbrot. Benoît B.
Mandelbrot[note 1][note 2] (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician, noted for developing a "theory of roughness" in nature and the field of fractal geometry to help prove it, which included coining the word "fractal". He later discovered the Mandelbrot set of intricate, never-ending fractal shapes, named in his honor.[7] While he was a child, his family fled to France in 1936 to escape the growing Nazi persecution of Jews. After World War II ended in 1945, Mandelbrot studied mathematics, graduating from universities in Paris and the U.S., receiving a masters degree in aeronautics from Caltech. He spent most of his career in both the U.S. and France, having dual French and American citizenship.
Benoit Mandelbrot: Fractals and the art of roughness. I AM COMPLEX. Mandelbrot set. Initial image of a Mandelbrot set zoom sequence with a continuously colored environment Mandelbrot animation based on a static number of iterations per pixel.
A Radical Mind. Posted 10.01.08 NOVA "Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
" So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "rough," he says. To study and learn from such roughness, for which he invented the term fractal, Mandelbrot devised a new kind of visual mathematics based on such irregular shapes. Digital Art Gallery. Visions 3D - Rendered Reality. 3D Commune Webring. Fractal Artists Webring. InterSpace 3D. Fractal Art Network. AuthorPOINT's flash presentation. Fractals: A Sense of Scale. By Peter Tyson Posted 10.01.08 NOVA.
Twin Prime Conjecture. PBS Airdate: January 10, 2006 ROBERT KRULWICH: Our next story concerns prime numbers.
It's a mystery that's been around for 2,300 years, since the days of the great mathematician Euclid. Now a prime number, for those of you who have forgotten, is a number which can only be divided by itself and one. Hunting the Hidden Dimension. NOVA explores the fascinating world of fractals and looks at how they can be used to better understand everything from coastlines and rainforests to weather systems and human physiology.
Seven Prime Questions. Fractal posters - online fractal generator. Zen Mandelbrot Offline Fractal Generator. Developer: Zen Dog Software License: Shareware Windows 98 / ME / 2000 / XP / 2003 / Vista.
Design a Fractal. Freeware fractal generator - Features. Sterling2 download page. Sterling2 is based on Sterling, a fractal-generating program written in 1999 by the redoubtable Stephen C.
Ferguson. In mid-2007 I contacted Stephen, as I thought that Sterling was an excellent program that lacked one key feature - a formula editor. He told me that adding a formula editor would be a huge job and that in any case the development environment to compile all the parts of Sterling was no longer available, as it is obsolete. However, he encouraged me to do the next best thing, which was to change the formulae in the program. With his help I set up the development environment on my PC and was able to recompile Sterling and to make changes to just one part of the program, ie the formulae. Between June 2007 and August 2008, I spent some 100 to 200 hours changing formulae (that's the quick part) and then testing them to see which ones produced interesting images. Download Sterling2 for Windows by clicking below (437 kbytes) The zip file contains brief instructions.
Fractint Development Team Homepage. Apophysis.org. FRACTINT Homepage. Download Fractint 18.21 Free - Create your fractals with the help of this tool. The beauty and complexity of fractals has ensnared many users and not necessarily those with inclinations towards the exact sciences.
Nonetheless, looking deep inside one or customizing its parameters would not be possible without the help of a utility like Fractint. Dull interface for splendid shapes With the package unwrapped, you can start the application immediately as it doesn't have to be installed and comes with all the necessary dependencies. The looks are certainly not its strong point, but its practicality compensates for that. Loading files is possible only if they are in GIF format, but opening a fractal is done by selecting the desired formula from the dedicated menu. Customizable fractals and views. Ultra Fractal: Advanced Fractal Software for Windows and Mac OS X. Eye of the Dragon. Fractal 3d. Electric Sheep 2-hour Fractal Animation. Best fractals zoom ever. Process (Fractal)
Zoom MandelBox 3D. HD LAVA LAMP Ambient Video Wall Art. Fractal. Figure 1a. The Mandelbrot set illustrates self-similarity. As the image is enlarged, the same pattern re-appears so that it is virtually impossible to determine the scale being examined. Figure 1b. The same fractal magnified six times. Figure 1c. Figure 1d. Fractals are distinguished from regular geometric figures by their fractal dimensional scaling. As mathematical equations, fractals are usually nowhere differentiable.[2][5][8] An infinite fractal curve can be conceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface.[7]:48[2]:15.
Fractals. Fractals From Wikibooks, open books for an open world The latest reviewed version was checked on 19 March 2014. There are template/file changes awaiting review. Jump to: navigation, search “What I cannot create, I do not understand.” — Richard P. Introduction[edit] List of fractals by Hausdorff dimension. Deterministic fractals[edit] Random and natural fractals[edit] See also[edit] Notes and references[edit] Further reading[edit] Crystal. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.
The word crystal is derived from the Ancient Greek word κρύσταλλος (krustallos), meaning both “ice” and “rock crystal”,[1] from κρύος (kruos), "icy cold, frost".[2][3] Examples of large crystals include snowflakes, diamonds, and table salt. Golden ratio. Line segments in the golden ratio In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. Expressed algebraically, for quantities a and b with a > b > 0, The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean.[1][2][3] Other names include extreme and mean ratio,[4] medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut,[5] and golden number.[6][7][8] Snowflake. Fractal flame. Fractal flames differ from ordinary iterated function systems in three ways: Random walk. Sacred geometry.
As worldview and cosmology[edit] Turbulence. Fractal art. Fractal art is a form of algorithmic art created by calculating fractal objects and representing the calculation results as still images, animations, and media. Patterns in nature. Natural patterns form as wind blows sand in the dunes of the Namib Desert. Complexity. Mandelbulb. Fractal. Please look also at Category Fractals page Overview[edit] File:Fractal.ogg.