import numpy as np


def mandel(xrange, yrange, maxiter):
    if xrange.ndim != 1 or yrange.ndim != 1: 
        raise ValueError("need 1D ranges for x and y")

    ny = yrange.size
    nx = xrange.size

    niter = np.zeros([ny, nx], dtype=np.int)

    for i in range(ny):
        y0 = yrange[i]
        for j in range(nx): 
            x0 = xrange[j]

            # we do not manipulate python complex numbers, but write
            # the complex operations explicitly
            
            # initial value
            x = x0
            y = y0

            for k in range(maxiter):
                x2 = x * x
                y2 = y * y 
                if x2 + y2 > 4: # check absolute value
                    break 

                # update series
                y = 2 * x * y + y0
                x = x2 - y2 + x0

            # maxiter or last iteration 
            niter[i, j] = k
                
    return niter