Mandelbrot set
Videos
The Mandelbrot set is a two-dimensional set. It is defined in the complex plane as the complex numbers c for which the function f c = z 2 + c does not diverge to infinity when iterated starting at z =
The Mandelbrot set plotted on the complex plane within a continuously colored environment
Gap between the "head" and the "body", also called the "seahorse valley"
Double-spirals on the left, "seahorses" on the right
Julia set
Videos
In complex dynamics, the Julia set and the Fatou set are two complementary sets defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby
Mandelbrot set
…f c ( f c ( 0 ) ) | , … crosses an arbitrary threshold. If c is held constant and the initial value of z is varied instead, the corresponding Julia set for the point c is obtained. The Mandelbrot set is well-known, even outside mathematics, for how it exhibits complex fractal structures when visualized…
The equipotential lines for iteration towards infinity
Three-dimensional rendering of Julia set using distance estimation
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