This is a minor change, with a 50% improvement to @gareth's answer. Changing 

`escaped = abs(z_live) > threshold` to 

`escaped = z_live.real**2 + z_live.imag**2>threshold**2`

while less nice looking is about 50% faster because it saves a square-root of all the elements.

To time it, I used

    t1 = time()
    image = julia_set(mapping=mapping,
                      min_coordinate=-1.5 - 1j,
                      max_coordinate=1.5 + 1j,
                      iterations_count = 255,
                      width=1920,
                      height=1080)
    print(time() - t1)

Before: 3.16s
After 3.21s