That means, for every point on a mandelbrot set, you can generate a Julia set. Although both sets are continuous functions in the complex plane, they are usually rendered by sampling an even grid (pixels), and if the point is a prisoner point, it is rendered black. It is generated by sampling the center point of all possible Julia sets. The Mandelbrot set is the set if all fully connected Julia sets. A disconnected Cantor dust of points (for more on Cantor dust - If the center point (0,0) of a Julia set is a prisoner point, then the Julia set is completely connected if it is not a prisoner point the Julia set is a Cantor dust. There is a full Julia set for all possible values of C C is a 2-dimensional value on the complex plane.ġ. You can clearly see that it is formed of thousands of tiny spheres.Ī Julia set is the set of points on the complex plane that when squared and added iteratively to a constant (C), the 'prisoner' points fail to leave a circle of radius 2.
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