# Mandelbrot

Mandelbrot & Julia Fractals

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Mandelbrot Fractal

Fullscreen Gigapan Viewer: Mandelbrot Fractal
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MATLAB Central - Large fractal images generated in MATLAB -

Mathematical imagery by Jos Leys.

Fractals
Fractals Here are some pictures from my July 13, 2004 talk at the Texas State Honors Summer Math Camp. All images are 2048 x 1536 and in PNG format. Mandelbrot Set Julia Sets

Paperbrot

Mandelbrot Cauliflower
Mandelbrot cauliflower Shopping in October, 2006 at Volante Farm, in Needham, MA, I came across this unusual cauliflower. It reminded me of a picture I saw somewhere of a piece of the Mandelbrot set. I doubt that I can find the picture I remember.

Mandelbrot set from moire patterns
Made by Bernard Helmstetter with the following procedure: First draw a 4000x3000 image of the Mandelbrot set, with two different colors (green and blue for example) for the outside: Image:Mandelbrot set from moire patterns first step.png. The colors have been chosen based on the values of an expression of the form ((int) floor(f(r))) & 1, where r is the potential, and f is a function varying rapidly, so that moiré patterns appear. Then, edit under gimp to extract interesting features. The first important steps were: gaussian blur (radius = 2px), decompose to HSV and keep only V, invert colors, dilate, erode twice. Click on a date/time to view the file as it appeared at that time.

Benoît Mandelbrot
Benoît Mandelbrot is not an artist in the usual sense of the word. He doesn’t work with oils, watercolors, pastels or colored pencils, yet he has created work of extraordinary beauty. Benoît Mandelbrot is a mathematician.

Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah The Mandelbrot Set. Note: All of the Mandelbrot pictures on this page were generated with the applet on this page! You can click on any of them to see a large version, and you can use the applet to generate those very same pictures, or similar pictures all your own! The first picture ( No1 ) shows a small part of the Mandelbrot set (which is rendered in red). List of Contents
The Mandelbrot Set

Mandelbrot Galaxy Wallpaper - Fractal Wallpaper Art Gallery, Fractals by Vicky

Benoit Mandelbrot Fractal Art Contest 2007

Mandelbrot Maps

Mandelbrot Set - Labix
Introduction These snippets compute and draw a graphic representation for the classical Mandelbrot set fractal. Results Running under pygame: Running under a Nokia 770 with pymaemo (also pygame):

David Deutsch on knowledge as crafted self-similarity « Entersection

A Short And Entertaining Introduction to Fractals usually one's first response to fractals is simply this: they are beautiful! indeed, they are visually arresting, and there are many reasons why. perhaps one reason is that they exhibit extreme levels of symmetry, a property we have gravitated toward throughout human history, whether it be in our architectural designs, in our scientific theories, in our religions, or even in the facial structures of the opposite sex. another reason could be that the same self-replicative patterns can be found strewn throughout our natural universe, in vapor trails, snail shells, evergreens, cauliflowers, and snowflakes ... just to name a few. but perhaps most enticing is a reason most people would never guess -- mathematical brevity. many of these stunning patterns are governed by very simple-looking equations consisting of only a few symbols!
[ wu :: fractals ]

[ wu :: fractal gallery ]

Fractal Art by Paul DeCelle

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of points in the complex plane such that the corresponding Julia set is connected and not computable. "The" Mandelbrot set is the set obtained from the quadratic recurrence equation

## Mandelbrot Set

The Mandelbrot Set : Good Math, Bad Math
The most well-known of the fractals is the infamous Mandelbrot set. It’s one of the first things that was really studied *as a fractal*. It was discovered by Benoit Mandelbrot during his early study of fractals in the context of the complex dynamics of quadratic polynomials the 1980s, and studied in greater detail by Douady and Hubbard in the early to mid-80s. It’s a beautiful example of what makes fractals so attractive to us: it’s got an extremely simple definition; an incredibly complex structure; and it’s a rich source of amazing, beautiful images. It’s also been glommed onto by an amazing number of woo-meisters, who babble on about how it represents “fractal energies” – “fractal” has become a woo-term almost as prevalent as “quantum”, and every woo-site that babbles about fractals invariably uses an image of the Mandelbrot set. It’s also become a magnet for artists – the beauty of its structure, coming from a simple bit of math captures the interest of quite a lot of folks.

How Mandelbrot's fractals changed the world
18 October 2010Last updated at 14:15 By Jack Challoner Science writer Fractals have become a common sight, thanks to computer imagery In 1975, a new word came into use, when a maverick mathematician made an important discovery.