Even the fractal pattern that bears his name is created from Julia sets: indeed, focus in on any boundary point of the Mandelbröt set, and it’s functionally the same as a Julia set.

who loves the quasi-organic mathematical patterns of the Mandelbrot set and Julia set fractals, Frax is great. The colors and textures put every pixel on my third-generation iPad to use.

This time, select 'Mandelbrot / Julia Sets' from 'Fractals'. A settings window will open, click OK. Then, a figure expressing the Mandelbrot set as a fractal figure was generated as follows.

If you want to learn more about these fascinating shapes, check out the Mysteries of Fractal app. The highly interactive app takes users through the basic principles of Julia set fractals in a fun ...

then that point IS in the Julia set. Julia sets can be simple (like a circle) or extremely complicated like a fractal. See the W00 course notes on Julia sets for more information on Julia sets. See ...

But you don’t have to be a Christian to be awed by the fractal geometries found in nature. Mandelbrot himself said that plotting Julia Set solutions never felt like invention to him: I never had ...

That algorithm analyzes features of the original polynomial, like its degree (the highest number that appears as an exponent) and its coefficients, and outputs another fractal shape that DeMarco and ...