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  2. Plotting algorithms for the Mandelbrot set - Wikipedia

    en.wikipedia.org/wiki/Plotting_algorithms_for...

    Every pixel that contains a point of the Mandelbrot set is colored black. Every pixel that is colored black is close to the Mandelbrot set. Exterior distance estimate may be used to color whole complement of Mandelbrot set. The upper bound b for the distance estimate of a pixel c (a complex number) from the Mandelbrot set is given by [6] [7] [8]

  3. Mandelbrot set - Wikipedia

    en.wikipedia.org/wiki/Mandelbrot_set

    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. [43] 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 ...

  4. File:Mandelbrot set from powers 0.05 to 2.webm - Wikipedia

    en.wikipedia.org/wiki/File:Mandelbrot_set_from...

    English: This video is comprised of frames illustrating each of the powers of the mandelbrot set from 0.05 to 2, incrementing by 0.05 with each iteration. Date 14 May 2014, 11:41:42

  5. Multibrot set - Wikipedia

    en.wikipedia.org/wiki/Multibrot_set

    In mathematics, a Multibrot set is the set of values in the complex plane whose absolute value remains below some finite value throughout iterations by a member of the general monic univariate polynomial family of recursions. [1] [2] [3] The name is a portmanteau of multiple and Mandelbrot set.

  6. Polynomial lemniscate - Wikipedia

    en.wikipedia.org/wiki/Polynomial_lemniscate

    An interesting example of such polynomial lemniscates are the Mandelbrot curves. If we set p 0 = z, and p n = p n−1 2 + z, then the corresponding polynomial lemniscates M n defined by |p n (z)| = 2 converge to the boundary of the Mandelbrot set. [2] The Mandelbrot curves are of degree 2 n+1. [3]

  7. Mitsuhiro Shishikura - Wikipedia

    en.wikipedia.org/wiki/Mitsuhiro_Shishikura

    He proved [4] that the boundary of the Mandelbrot set has Hausdorff dimension two, confirming a conjecture stated by Mandelbrot [5] and Milnor. [6] For his results, he was awarded the Salem Prize in 1992, and the Iyanaga Spring Prize of the Mathematical Society of Japan in 1995. More recent results of Shishikura include

  8. Is there already a College Football Playoff controversy ...

    www.aol.com/sports/college-football-playoff...

    The College Football Playoff selection committee enters its final two weeks of deliberation with a host of consequential decisions thrust on the 13 members.

  9. Tricorn (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Tricorn_(mathematics)

    A tricorn, created on a computer in Kalles Fraktaler. Tricorn zoom onto mini-tricorn Multicorns with the power going from 1 to 5. In mathematics, the tricorn, sometimes called the Mandelbar set, is a fractal defined in a similar way to the Mandelbrot set, but using the mapping ¯ + instead of + used for the Mandelbrot set.