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  "body": "\n## Summary\n\nQuadratic polynomial dynamics is the study of the iteration of the maps $f_c(z) = z^2 + c$ on the complex plane.\nUp to an affine change of variable, every quadratic polynomial is one of these maps.\nIt is the simplest nontrivial case of [[complex dynamics|BQQZ0ZCGQF]] and the testing ground for most of its ideas.\nIts parameter space is organised by the [[Mandelbrot set|QSWSVYRCS1]].\n\n## Explanations\n\n### L1 human\n\nTake the rule $z \\mapsto z^2 + c$ for a fixed complex number $c$ and follow the orbit of each starting point.\nSome orbits run off to infinity and others stay bounded.\nThe bounded ones form the filled Julia set, and its border is the [[Julia set|5M4S7P04GR]].\nFor $c = 0$ the filled Julia set is the closed unit disc.\nFor $c = -1$ it is a shape made of infinitely many touching blobs, called the basilica.\nThe single orbit of $0$ already decides whether the Julia set is one piece or a cloud of dust.\n",
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