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Mandelbrot Set

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The Mandelbrot set is a fractal consisting of all complex numbers c such that the corresponding Julia set of the function f(z) = z^2 + c is connected.

Mandelbrot set is a college-level concept that would be first encountered in a dynamical systems course.

Prerequisites

Dynamical System: A dynamical system is a description of the way a complex system changes over time.
Fractal: A fractal is an object or quantity that displays self-similarity on all scales.
Recurrence Relation: A recurrence relation is a mathematical relationship expressing the members of a sequence as some combination of their predecessors.

Classroom Articles on Dynamical Systems (Up to College Level)

  • Chaos