Mandelbrot Set

a

b

xn+1 = xn2 - yn2 + a

yn+1 = 2xnyn + b

zn+1 = zn2 + c

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"The most complicated mathematical object ever seen"

Only the bounded orbits are shown

Boundary is fractal with dimension 2

All periods are represented somewhere

Chaotic orbits are very rare (probability zero?)