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Mandelbrot set
Mandelbrot set
The Mandelbrot set is a complex mathematical object that was discovered by the mathematician Benoit Mandelbrot in 1979. It is a set of complex numbers that have a particular property, and is named after Mandelbrot in recognition of his discovery.
It is a set of complex numbers that are generated by iterating a simple formula repeatedly.
The formula is:
Here, Z is a complex number, and C is a constant complex number. We start with Z₀ = 0, and we apply the formula to generate a sequence of numbers: Z₁, Z₂, Z₃, and so on.
If the sequence of numbers stays bounded (i.e., doesn't get too large), then the complex number C is said to be in the Mandelbrot set. If the sequence diverges (i.e., gets arbitrarily large), then C is not in the Mandelbrot set.
The Mandelbrot set is famous for its intricate and complex structure, which is characterized by the presence of self-similarity and fractal geometry. The set is often depicted using a visual representation known as the "Mandelbrot set fractal," which displays the complex structure of the set in a colorful and visually striking way.
The Mandelbrot set has important applications in fields such as chaos theory, computer graphics, and fractal geometry. It is a fascinating object of study for mathematicians and scientists alike, and continues to inspire new research and discoveries to this day.
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