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Mandelbrot Fractal Explorer

The application below allows you to explore two different Mandelbrot set fractals -- the regular Mandelbrot set and the "cubic" Mandelbrot set. By zooming into the multicolored areas around the edges of each Mandelbrot set, you can discover a whole world of vibrant and beautiful patterns. To zoom, position your mouse at the center of the area you would like to zoom into and click and drag to change the size of the zoomed area. You can drag the color slider to cycle through different colors, which can help to accentuate the pattern. You can use the Undo and Redo buttons to step through your complete history of changes, and the cubic and regular Mandelbrot set buttons on the right to reset your view to either set, completely zoomed out.

If you enjoy this activity, be sure to try the Fractal Explorer filter in SketchRay, our digital image explorer for OS X and Windows. You can use it to explore the regular and cubic Mandelbrot sets in the same way as above, but it also allows you to create and save fractal images at any size, blend them with other images, or process them with additional dynamic filters. Download SketchRay for free!

See examples of fractal images created with SketchRay

See examples of fractal images created with SketchRay

The following images were all created in SketchRay using its Fractal Explorer filter to generate Mandelbrot fractal patterns just like the fractal explorer above. SketchRay's editing tools, additional filters, and layer system were also used extensively to enhance those patterns and create these stunning images. Learn how to create a complex layered fractal image in SketchRay with this tutorial.









Learn more about fractals and the Mandelbrot Set

Learn more about fractals and the Mandelbrot Set

The Mandelbrot Set

The Mandelbrot Set is a set of complex numbers discovered in 1979 by mathematician Benoit Mandelbrot. When plotted and colored on a two dimensional plane like a computer screen, it creates the famous Mandelbrot set fractal. The term "Fractal", also coined by Benoit Mandelbrot, refers to a mathmatical construct or natural phenomenon that has a repeating, "self similar" pattern at different scales. A fantastic example of a fractal in nature is the Romanesco Brocolli -- it is "self similar" because each peak of the brocolli is made up of smaller copies of itself (see picture below). Mandelbrot noticed these patterns in nature and sought to create a form of geometry that could model them. It was in this process that he discovered the Mandelbrot set.

Fractals in Nature

Nature is filled with examples of fractals. From the branching and leaves of trees and plants, to the contour of a coastline, to the shape of a snowflake. Here are some examples of self similar patterns in nature:

Fern

Romanesco Broccoli

Sand Erosion Patterns

Snowflake

Mandelbrot Fractals

In the application above, you got to explore two different Mandelbrot sets -- the regular Mandelbrot set and the "cubic" Mandelbrot set. The cubic Mandelbrot is so named because the mathematical expression that defines it raises one value to a power of three rather than a power of two as in the regular Mandelbrot set. By zooming into the multicolored areas around the edges of each Mandelbrot set, you can discover a whole world of vibrant, beautiful, self similar patterns.


Mandelbrot Set

Cubic Mandelbrot Set

Mandelbrot Zoom

Mandelbrot Zoom

Cubic Mandlebrot Zoom
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