我目前正在使用PhotoImage和tkinter逐像素绘制Mandelbrot集。我基本上是直接使用没有修改的算法。有没有使计算更快的方法？也许快速填充大面积的颜色，或者预先计算常数？

部分代码：

ITERATIONS = 50
WIDTH, HEIGHT = 600, 600
CENTER = (-.5, 0)
DIAMETER = 2.5

def mandel(c):
    z = 0
    for i in range(ITERATIONS):
        z = z**2 + c
        if abs(z) > 2:
            return i     
    return ITERATIONS

root = Tk()
canvas = Canvas(root, width=WIDTH,height=HEIGHT)
canvas.pack()
img = PhotoImage(width=WIDTH, height=HEIGHT)
canvas.create_image((WIDTH/2, HEIGHT/2), image=img, state="normal")


real = CENTER[0] - 0.5 * DIAMETER
imag = CENTER[1] - 0.5 * DIAMETER

def color(i):
    colors = ("#0000AA", "#88DDFF", "#FF8800", "#000000")
    if i == ITERATIONS:
        return colors[-1]
    else:
        choice = (i//2) % len(colors)
    return colors[choice]

for x in range(WIDTH):
    for y in range(HEIGHT):
        i = mandel(complex(real, imag))

        img.put(color(i), (x, HEIGHT-y))

        imag += DIAMETER / HEIGHT
    imag = CENTER[1] - 0.5 * DIAMETER
    real += DIAMETER / WIDTH

mainloop()