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: Zn = Zn-12 + 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 ...

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 reve ...

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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) = x2 – 0.75. We will iterate this function when initially applied to an initial value of x, say x = a0. Let a1 denote the first iterate f(a0), let ...

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. 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 ...

Selected images created by *you* using Mandelbrot Explorer are available at the Mandelbrot Explorer Gallery Page. Zoom Factor : ZoomIn x16ZoomIn x8ZoomIn x4ZoomIn x2NoneZoomOut x2ZoomOut x4ZoomOut x8ZoomOut 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 Mandelbrot Exhibition, part of the Virtual Museum of Computing Panagiotis Christias / Last change 17 Aug 94 NTUA/SoftLab Home Page

The Mandelbrot Set Produced by Andy Burbanks Zoom on the Mandelbrot Set The following pictures show the Mandelbrot set at various magnifications. In each successive picture the magnification increases by a factor of five (the width 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. UP: Gallery | Mathematical Sciences | Loughborough University webmaster

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 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 ...

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 Mandelb ...