111 - Mandelbrot Set

Generate an image of the Mandelbrot Set:

The algorithm is the following:

• choose a grid of points in the imaginary plane, for example:

  • 1500 values from x = -2.0 to 1.0, and

  • 1000 values from y = -1.0 to 1.0

• we will iterate though all of those points and for each:

  • create a complex number c corresponding to the point (and initial value of z=0)

  • while z is less than 2 units from the origin and the number of iterations for this point is less than 100

    • calculate \(z = z^2 + c\)

    • track the number of iterations for the original point c before one of the two conditions is no longer satisfied

• Make a plot of the iterations for all points in the original grid (hint: use plt.imshow with cmap=’coolwarm’, for example)