Arithmetic Dynamics
Iteration of rational maps z → z² + c over ℂ and p-adic fields
Mandelbrot Parameter Plane
Map:
z² + c (Mandelbrot)
z³ + c
z² + c/z
c·sin(z)
Newton: z³−1
Max iter
80
Render
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Julia Set & p-adic Dynamics
f(z) = z² + c | p-adic orbit coloring
p (prime):
p=2
p=3
p=5
p=7
p=11
p-adic Orbit
Click on Mandelbrot to pick c, see Julia set and p-adic orbit