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2015年5月22日 · If this is true, your "Mandelbrot set" would be dense in the plane and you would probably not see anything on your picture. $\endgroup$ – Lukas Geyer Commented May 22, 2015 at 20:06

2022年10月1日 · In this picture some equipotentials around the Mandelbrot set are plotted, labelled by approximate length. As you can see, at first the lengths decrease as you get closer, but it reaches a minimum at about $14.9$ before increasing rapidly because the curves have to wriggle a lot (the shape of the Mandelbrot set is complicated).

2015年4月29日 · The Mandelbrot set is defined as follows: given the function f(z, c) = z 2 + c, a number z in the complex plane is in the Mandelbrot set if and only if the sequence defined by z 0 = z, z n+1 = f(z n, z 0) is bounded. There are numerous programs that draw images computed from such definitions, including my own "HTML 5 Fractal Playground ...

You seem to get the most "natural" looking images (i.e., the ones most like the usual Mandelbrot and Julia sets) if you stick to nice, well-behaved complex-valued functions. If you want to be picky about it, the Mandelbrot set really ought to be the set …

2018年4月17日 · $\begingroup$ @Adam afaict the (English version of the) book just states 2 facts that are already known: 1. the golden spiral is a particular logarithmic spiral; and 2. some logarithmic spirals are in the Mandelbrot set. This however does not answer the question of whether there is a golden spiral in the Mandelbrot set. $\endgroup$ –

2013年6月14日 · The usual proof that the Mandelbrot set is connected constructs - somewhat miraculously, if you are not used to these things - the Riemann map (conformal isomorphism) between the complement of the Mandelbrot set and the complement of the closed unit disk. The proof is not so hard if you know complex analysis.

The julia set associated to the center of the main cardioid of the mandelbrot set is a circle, so I assume the julia sets associated to the main cardioid of a minibrot will be a julia set built of circles (like pictured): This needs proof but it seems like it would be too difficult so I am happy to leave this unproved for now (but I would like ...

2011年12月12日 · I decided to learn about the Canvas object in javascript by implementing a display of the Mandelbrot Set. I am mimicking the Mandelbrot psuedocode found on wikipedia. The thrust of it is that the number of iterations it takes for a point to diverge is proportional to the color that is assigned to that point.

2018年1月27日 · That said, there are results (mainly due to JC. Yoccoz, a Fields medallist) proving that the Mandelbrot set is locally connected at every point except possibly some special points (called infinitely renormalizable parameters; roughly speaking they are those points that are in infinitely many nested small copies of the Mandelbrot set).