The Mandelbrot Set
The Mandelbrot set is defined by iterating z = z² + c for each point c in the complex plane. Points where the iteration stays bounded belong to the set. The boundary is infinitely complex — a fractal with dimension 2.
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Interactive Mandelbrot and Julia set generation with zoom
zₙ₊₁ = zₙ² + c|zₙ|² > 4 → escaped at iteration iThe Mandelbrot set is defined by iterating z = z² + c for each point c in the complex plane. Points where the iteration stays bounded belong to the set. The boundary is infinitely complex — a fractal with dimension 2.
Each point c in the complex plane defines a corresponding Julia set. Points inside the Mandelbrot set produce connected Julia sets; points outside produce disconnected "Fatou dust" patterns.