Here's a fun fact about the Mandelbrot set, which I will communicate in Python in the hope that you can have a little fun witnessing the results:

  def N(eps):
    c = -0.75 + eps*1j
    n = 0
    z = 0
    while abs(z) < 2:
      z = z*z + c
      n += 1
    return n

  [N(eps) for eps in [0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001]]