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Mandelbrot

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		The Mandelbrot Set ^Votes:0 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 Applet The Drawing Algorithm The Control Panel The Text Fields The x and y ranges The size of the drawing area The crucial parameter, maxit The Mouse Position The Resolution Setting Status Frequency The Aspect Ratio Fast or Safe? The Examples Menu Quitting The Drawing Window The Status Panel The Color Scheme and the Read More Go to Site


		Mandelbrot Explorer ^Votes:0 Mandelbrot Explorer Selected images created by you using Mandelbrot Explorer are available at the Mandelbrot Explorer Gallery Page. Please consider that this free service takes up a lot of cpu because images are calculated on the fly. If you want this service to continue to exist, don't run many instances of the mandelbrot explorer at the same time. Thank you, the webmaster . Zoom Factor : ZoomIn x16 ZoomIn x8 ZoomIn x4 ZoomIn x2 None ZoomOut x2 ZoomOut x4 ZoomOut x8 ZoomOut x16 Set the Zoom Factor as desired and then click at the point you like to zoom in (or out) in the image area above. Drawing Area : X Min : X Max : Y Min : Y Max : Commands : Alternatively, you can set the desired Drawing Area and press the ``Draw New Area'' button to see it. More Fractals can be found at the Mandelb Read More Go to Site

		Fabio Cesari: Fractal Explorer ^Votes:0 What is the Mandelbrot set? The Mandelbrot set is the domain of convergence of the series built up by the complex sequence defined by the recursion law: Z n = Z n-1 2 + C . In other words, with a simple algorithm it is possible to separate the points of the complex plane into two categories: points inside the Mandelbrot set points outside the Mandelbrot set The image below shows a portion of the complex plane. The points of the Mandelbrot set have been coloured black. It is also possible to assign a colour to the points outside the Mandelbrot set. Their colour depends on how many iterations have been required to determine that they are outside the Mandelbrot set, and it can be interpreted as their "distance" from the Mandelbrot set. How can I build the Mandelbrot set? Pick a point on the c Read More Go to Site

		Introduction to the Mandelbrot Set ^Votes:0 This page has been moved to http://www.ddewey.net/mandelbrot/ . The version here will no longer be maintained or updated. Please update your links. Introduction to the Mandelbrot Set A guide for people with little math experience. By David Dewey According to Web-Counter you are visitor number since November 02, 1996. The Mandelbrot set, named after Benoit Mandelbrot, is a fractal . Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involvi Read More Go to Site

		Julia and Mandelbrot Sets ^Votes:0 Julia and Mandelbrot Sets David E. Joyce August, 1994. Last updated May, 2003. Function Iteration and Julia Sets Gaston Julia studied the iteration of polynomials and rational functions in the early twentieth century. If f ( x ) is a function, various behaviors can arise when f is iterated. Let's take, for example, the function f ( x ) = x 2 0.75. We will iterate this function when initially applied to an initial value of x , say x = a 0 . Let a 1 denote the first iterate f ( a 0 ), let a 2 denote the second iterate f ( a 1 ), which equals f ( f ( a 0 )), and so forth. Then we'll consider the infinite sequence of iterates a 0 , a 1 = f ( a 0 ), a 2 = f ( a 1 ), a 3 = f ( a 2 ), ... It may happen that these values stay small or perhaps they don't, depending on the initial value a 0 . Read More Go to Site

		Mandelbrot and Julia Set Explorer ^Votes:0 Julia and Mandelbrot Set Explorer David E. Joyce For background on Julia and Mandelbrot sets, see the introduction. There is detailed help available for using this form. For more information on complex numbers, see Dave's Short Course on Complex Numbers . Also, check out the Applet to explore the Mandelbrot set . I recently stumbled upon StumbleUpon that helps you discover and share great websites. You can create a public blog of websites you like and find other websites like those you like. You'll need either a Firefox browswer or a Mozilla 1.5-1.8 complient browser. Mandelbrot Set : x in [-1.0,2.0]; y in [-1.5,1.5]. Parameters Clicks on the Mandelbrot set image will get a Julia set magnify the Mandelbrot set by a factor of Alternate Mandelbrot parameter plane mu lambda (mu = lambda^2/4-l Read More Go to Site

		The Mandelbrot set ^Votes:0 The Mandelbrot set Produced by Andy Burbanks The following pictures show the Mandelbrot set at various magnifications. In each successive picture the magnification increases by a factor of five (the width w of the region shown is indicated below each picture). The centre of the picture is the same in each case (c = -0.7454265 + 0.1130090i). (a) w=4 (b) w=0.8 (c) w=0.16 (d) w=0.032 (e) w=0.0064 (f) w=0.00128 (g) w=0.000256 (h) w=0.0000512 (i) w=0.00001024 In the final picture, a small "copy'' of the whole set is seen, surrounded by tendrils. Back to: Gallery home Home page webmaster Read More Go to Site

		The Mandelbrot Set ^Votes:0 The Mandelbrot Set JDK 1.0 version If you were using a Web browser with Java, you could explore the Mandelbrot set here. This is a little applet (which should appear as a pop-up) I wrote that lets you explore the Mandelbrot set. The Mandelbrot set is a type of infinitely complex mathematical object known as a fractal. No matter how much you zoom in, there is still more to see. There are many strange and beautiful sights to see when you explore the Mandelbrot set, ranging from the sublime to the psychedelic. In my applet, you can set the area you want to zoom in on by holding down the mouse button and dragging on the picture. You can also set the coordinates that you want to look at in the four text boxes. Press "Zoom In" when you are satisfied with the bounds you want to see. For instance, Read More Go to Site

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