How to do it...

Follow these steps to use Cython to greatly improve the performance of the code for generating an image of the Mandelbrot set:

1. Start a new file called cython_mandel.pyx in the mandelbrot folder. In this file, we will add some simple imports and type definitions:

# mandelbrot/cython_mandel.pyx

import numpy as np
cimport numpy as np
cimport cython
ctypedef Py_ssize_t Int
ctypedef np.float64_t Double

2. Next, we define a new version of the in_mandel routine using the Cython syntax. We add some declarations to the first few lines of this routine:

cdef int in_mandel(Double cx, Double cy, int max_iter):
    cdef Double x = cx
    cdef Double y = cy
    cdef Double x2, y2
    cdef Int i

3. The rest of the function is identical to the Python version of the function:

    for i in range(max_iter):
        x2 = x**2
        y2 = y**2
        if (x2 + y2) >= 4:
            return i
...