How to render Mandelbrot Set faster?

Question

I\'m currently drawing the Mandelbrot set pixel by pixel with PhotoImage and tkinter. I\'m using basically the algorithm directly with no modifications. Are there methods to

Answer 1

For a modest increase in speed (but not enough to offset the difference between a compiled language and an interpreted one), you can precalculate some of the values.

Right now, you're calculating DIAMETER / HEIGHT once per inner loop, and CENTER[1] - 0.5 * DIAMETER as well as DIAMETER / WIDTH once per outer loop. Do this beforehand.

len(colors) also won't change and can be replaced by a constant. In fact, I'd probably write that function as

def color(i):
    if i == ITERATIONS:
        return "#000000"
    else:
        return ("#0000AA", "#88DDFF", "#FF8800", "#000000")[(i//2) % 4]
        # are you sure you don't want ("#0000AA", "#88DDFF", "#FF8800")[(i//2) % 3] ?

Also, x**2 is slower than x*x (because the x**y operator doesn't shortcut for the trivial case of y==2), so you can speed that calculation up a bit.