Mandelbrot Set
Benoît Mandelbrot; earlier work by Robert Brooks and Peter Matelski
A simple iteration creates a boundary with extraordinary detail.
Fractals & infinity / Early 20th century
Julia Set
Repeated complex mappings produce intricate connected shapes or dust-like sets.
TRY THIS
Follow a branch toward finer detail and compare the pattern with the Mandelbrot parameter map.
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What is Julia Set?
Repeated complex mappings produce intricate connected shapes or dust-like sets.
What should I look for in Julia Set?
Follow a branch toward finer detail and compare the pattern with the Mandelbrot parameter map.
What explains Julia Set?
For a quadratic example, keep c fixed and iterate z → z² + c from different starting points. The Julia set marks the boundary between different long-term behaviors; the filled Julia set includes the points that do not escape.
Another way to see it
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Mandelbrot Boundary Detail
Benoît Mandelbrot and researchers in complex dynamics
A close view reveals spirals, branching filaments, and smaller structures.