Julia sets are complex fractals that arise from iterating a complex quadratic polynomial of the form $$f(z) = z^2 + c$$, where $$z$$ is a complex number and $$c$$ is a constant complex parameter. They showcase intricate patterns that vary dramatically based on the value of $$c$$, connecting deep mathematical concepts with beautiful visual representations, making them relevant in various applications, from computer graphics to natural phenomena.
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