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Fractal, by Paul Carlson (Image 4)

A Mandelbrot set of Newton's method solution for the equation z4+(c1)z2c=0

A Mandelbrot set of Newton's method solution for the equation z4+(c1)z2c=0 rendered by the Tangent Circles Method.

Fractal (self-similar shapes that repeat themselves on increasingly smaller-length scales) sets are used extensively in computer graphics to build interesting, "natural-looking" clouds, plants, landscapes, sea surfaces, etc. They are also used in medical applications, for example, to model organs (lungs) or blood vessel networks.

This fractal set was created by Paul Carlson, a computer programmer who has written at least a dozen fractal-generating programs over the years and his fractals have appeared in numerous published books.

Further information about the creation of this set can be found in the Science Direct story Two artistic orbit trap rendering methods for Newton M-set fractals.

To learn more about Carlson's fractal work and view other fractal images he created, visit The Paul Carlson Fractal Museum. (Date of Image: unknown) [Image 4 of 5 related images. See Image 5.]


Credit: ŠPaul Carlson

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