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XaoS is an interactive fractal zoomer program.It allows the user to continuously zoom in or out of a fractal in real-time. XaoS is licensed under GPL.The program is cross-platform, and is available for a variety of operating systems, including Linux, Windows, Mac OS X, BeOS and others.
The quaternion (4-dimensional) Mandelbrot set is simply a solid of revolution of the 2-dimensional Mandelbrot set (in the j-k plane), and is therefore uninteresting to look at. [44] Taking a 3-dimensional cross section at d = 0 ( q = a + b i + c j + d k ) {\displaystyle d=0\ (q=a+bi+cj+dk)} results in a solid of revolution of the 2-dimensional ...
English: Mandelbrot set. Initial image of a zoom sequence: Mandelbrot set with continuously colored environment. Coordinates of the center: Re(c) = -.7, Im(c) = 0; Horizontal diameter of the image: 3.076,9; Created by Wolfgang Beyer with the program Ultra Fractal 3. Uploaded by the creator.
Mandelbrot set rendered using a combination of cross and point shaped orbit traps. In mathematics, an orbit trap is a method of colouring fractal images based upon how close an iterative function, used to create the fractal, approaches a geometric shape, called a "trap". Typical traps are points, lines, circles, flower shapes and even raster ...
Original - Mandelbrot zoom in. Reason Simply an epic animation and a fantastic representation of the multiple layers of complexity and chaos that make up the Mandelbrot set. The user Slaunger suggested that a scaled up version of an earlier animation, made by user Zom-B would probably be worthy of being a featured image.
Media in category "Mandelbrot set (featured picture set)" The following 15 files are in this category, out of 15 total. Mandel zoom 00 mandelbrot set.jpg 2,560 × 1,920; 1.25 MB
1.2619: 2D Cantor dust: Cantor set in 2 dimensions. 1.2619: 2D L-system branch: L-Systems branching pattern having 4 new pieces scaled by 1/3. Generating the pattern using statistical instead of exact self-similarity yields the same fractal dimension. Calculated: 1.2683: Julia set z 2 − 1: Julia set of f(z) = z 2 − 1. [9] 1.3057
Once b is found, by the Koebe 1/4-theorem, we know that there is no point of the Mandelbrot set with distance from c smaller than b/4. The distance estimation can be used for drawing of the boundary of the Mandelbrot set, see the article Julia set. In this approach, pixels that are sufficiently close to M are drawn using a different color.