Complex dynamics
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Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on the case of algebraic dynamics, where a polynomia
Julia set
Mandelbrot set
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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 =
Complex dynamics
…in the sense that its Hausdorff dimension is not an integer. This occurs even for mappings as simple as f ( z ) = z 2 + c for a constant c ∈ C . The Mandelbrot set is the set of complex numbers c such that the Julia set of f ( z ) = z 2 + c is connected. There is a rather complete classification of the possible…
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