Sekino's Fractal Art Gallery 2D

The gallery comprises fractal images that can be plotted on a plane by standard programming routines described in Stories about Fractal Plotting. We classify the images into four groups:

§ 1. The Mandelbrot Set

The Classical Mandelbrot Set  

The picture shown above is an image given by the Mandelbrot equation zn+1 = zn2 + p and is similar to what Benoit Mandelbrot showed the mathematics world in 1980. The old black and white image vividly reveals a simple but probably the most important fact about the M set (Mandelbrot set): The pattern in a neighborhood of a point outside of the M set grows more and more complex without bound as the point gets nearer the boundary of the M set.

In fact, the M set conceals infinitely many intricate fractal patterns near its boundary. We show several of them here painted by the "true color" technology that became available in the 1990s.

Partying Cuttlefish

Blue Jays

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We often paint fractal images on nonplanar surfaces such as tori and spheres. More examples are shown in Gallery II

The Mandelbrot Set in Colors

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     Gallery 2D: The Mandelbrot Set Logistic Equation, Etc Julia Sets Newton Fractals
     Gallery 3D: Fractal Mountains and Forests Fantasy Landscapes Fractals on Nonplanar Surfaces