Skip to main content
Email Print Share

Fractal, by Paul Carlson (Image 3)

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 Ring Segments 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 3 of 5 related images. See Image 4.]

SORRY: THIS IMAGE IS NOT AVAILABLE IN HIGH RESOLUTION FORMAT

Credit: ŠPaul Carlson

General Restrictions:
Images and other media in the National Science Foundation Multimedia Gallery are available for use in print and electronic material by NSF employees, members of the media, university staff, teachers and the general public. All media in the gallery are intended for personal, educational and nonprofit/non-commercial use only.

Images credited to the National Science Foundation, a federal agency, are in the public domain. The images were created by employees of the United States Government as part of their official duties or prepared by contractors as "works for hire" for NSF. You may freely use NSF-credited images and, at your discretion, credit NSF with a "Courtesy: National Science Foundation" notation. Additional information about general usage can be found in Conditions.

Also Available:
Download the high-resolution JPG version of the image. (456 KB)

Use your mouse to right-click (Mac users may need to Ctrl-click) the link above and choose the option that will save the file or target to your computer.