Preparations

In order to prepare our journey into concurrent programming let’s prepare some functions, that help us in breaking down our workload.

To support the row by row thinking lets create an implementation working on a single row.

Here is the one for a naive approach.

def mandel_row(y, x_min, x_max, max_iterations, resolution):
    x = [
        x_min + (x_max - x_min) / (resolution - 1) * index
        for index in range(resolution)
    ]
    row = []
    for _x in x:
        c = complex(_x, y)
        c0 = c
        for iteration in range(max_iterations):
            c = c**2 + c0
            if abs(c) > 2.0:
                break
        row.append(iteration)
    return row

whilst this one uses a numpy approach to calculate the row.

def mandel_row(y_value, x_min, x_max, max_iterations, resolution):
    x = np.linspace(x_min, x_max, resolution)
    y = np.array([y_value])

    c = x + y[:, None] * 1j
    c0 = c.copy()
    iterations = np.zeros_like(c, dtype=np.uint)

    for iteration in range(max_iterations):
        mask = np.abs(c) < 2.0
        c[mask] = c[mask]**2 + c0[mask]
        iterations[mask] += 1
    return iterations[0,:]