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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

    A mosaic made by matching Julia sets to their values of c on the complex plane. The Mandelbrot set is a map of connected Julia sets. As a consequence of the definition of the Mandelbrot set, there is a close correspondence between the geometry of the Mandelbrot set at a given point and the structure of the corresponding Julia set. For instance ...

  4. Connectedness locus - Wikipedia

    en.wikipedia.org/wiki/Connectedness_locus

    Without doubt, the most famous connectedness locus is the Mandelbrot set, which arises from the family of complex quadratic polynomials : = + The connectedness loci of the higher-degree unicritical families, +

  5. Fractal-generating software - Wikipedia

    en.wikipedia.org/wiki/Fractal-generating_software

    A similar plot to the very first render by Benoit Mandelbrot Palette editor in Fractint. The generation of fractals by calculation without computer assistance was undertaken by German mathematician Georg Cantor in 1883 to create the Cantor set. [6] Throughout the following years, mathematicians have postulated the existence of numerous fractals.

  6. 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.

  7. Orbit trap - Wikipedia

    en.wikipedia.org/wiki/Orbit_trap

    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".

  8. Kalles Fraktaler - Wikipedia

    en.wikipedia.org/wiki/Kalles_Fraktaler

    Kalles Fraktaler is a free Windows-based fractal zoom computer program used for zooming into fractals such as the Mandelbrot set and the Burning Ship fractal at very high speed, utilizing Perturbation and Series Approximation. [1]

  9. Burning Ship fractal - Wikipedia

    en.wikipedia.org/wiki/Burning_Ship_fractal

    The difference between this calculation and that for the Mandelbrot set is that the real and imaginary components are set to their respective absolute values before squaring at each iteration. [1] The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy–Riemann equations .