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  2. Mandelbrot set - Wikipedia

    en.wikipedia.org/wiki/Mandelbrot_set

    The Mandelbrot set within a continuously colored environment. The Mandelbrot set (/ ˈ m æ n d əl b r oʊ t,-b r ɒ t /) [1] [2] is a two-dimensional set with a relatively simple definition that exhibits great complexity, especially as it is magnified.

  3. Plotting algorithms for the Mandelbrot set - Wikipedia

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

    The simplest algorithm for generating a representation of the Mandelbrot set is known as the "escape time" algorithm. A repeating calculation is performed for each x, y point in the plot area and based on the behavior of that calculation, a color is chosen for that pixel.

  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. External ray - Wikipedia

    en.wikipedia.org/wiki/External_ray

    An external ray is a curve that runs from infinity toward a Julia or Mandelbrot set. [1] Although this curve is only rarely a half-line (ray) it is called a ray because it is an image of a ray. External rays are used in complex analysis , particularly in complex dynamics and geometric function theory .

  6. Misiurewicz point - Wikipedia

    en.wikipedia.org/wiki/Misiurewicz_point

    Misiurewicz points in the context of the Mandelbrot set can be classified based on several criteria. One such criterion is the number of external rays that converge on such a point. [4] Branch points, which can divide the Mandelbrot set into two or more sub-regions, have three or more external arguments (or angles). Non-branch points have ...

  7. 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 .

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  9. 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". Typical traps are points, lines, circles, flower shapes and even raster ...

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