How I can make my Mandelbrot plotter faster?

Question

How I can make my Python program faster? This program calculates the Mandelbrot set and draws it with turtle. I think the problem is in the for loop. Maybe the steps are taking too much time.

import numpy as np
import turtle
turtle.ht()
turtle.pu()
turtle.speed(0)
turtle.delay(0) turtle.colormode(255)

i= int(input("iteration = "))
g = int(input("accuracy  = "))
xmin = float(input("X-min: "))
xmax = float(input("X-max: "))
ymin = float(input("Y-min: "))
ymax = float(input("Y-max: "))
cmode = int(255/i)

input("PRESS TO START")
for x in np.arange(xmin,xmax,1/g):
    for y in np.arange(ymin,ymax,1/g):
        c = x + y * 1j
        z = 0
        t = 1
        for e in range(i):
            z = z * z + c
            if abs(z) > 3:
                turtle.setx(g*c.real)
                turtle.sety(g*c.imag)
                turtle.dot(2,e*cmode,e*cmode,e*cmode)
                t = 0

        if t == 1:
            turtle.setx(g*c.real)
            turtle.sety(g*c.imag)
            turtle.dot(2,"black")

input("Calculated!")
turtle.mainloop()

Here is an example

Questions regarding performance are more likely to be answered on the Code Review. — Badda
Thank you! I am a new user here so thanks for your help. Did not know that. @Badda — akinoioi
First speed-up would be to add break following t = 0 (if the draw routine is triggered, you don't need to continue calculations for this point). Beyond that, Python just isn't terribly fast; you could try to push the calculations into Numpy like thesamovar.wordpress.com/2009/03/22/… (claims a 3x speed-up) or you could switch to a faster compiled language like Julia julialang.org (even the name is appropriate ;-) and they include a 20x speed-up on mandelbrot set as one of their benchmarks) — Hugh Bothwell
Do you continue to iterate after the function value has escaped? — Weather Vane
... one more intermediate step before switching languages: you could try Cython cython.org which lets you compile (statically typed) Python directly to native code. — Hugh Bothwell

cdlane cdlane · Accepted Answer · 2017-06-09T18:59:26

The following rework should be a hundred times faster than your original:

import numpy as np
import turtle

i = int(input("iteration = "))
g = int(input("accuracy  = "))
xmin = float(input("X-min: "))
xmax = float(input("X-max: "))
ymin = float(input("Y-min: "))
ymax = float(input("Y-max: "))

cmode = int(255 / i)

input("PRESS TO START")

turtle.hideturtle()
turtle.penup()
turtle.speed('fastest')
turtle.colormode(255)
turtle.setundobuffer(None)  # turn off saving undo information

turtle.tracer(0, 0)

for x in np.arange(xmin, xmax, 1 / g):
    for y in np.arange(ymin, ymax, 1 / g):
        c = x + y * 1j
        z = 0
        t = True

        for e in range(i):
            z = z * z + c

            if abs(z) > 3.0:
                turtle.setposition(g * c.real, g * c.imag)
                rgb = e * cmode
                turtle.dot(2, rgb, rgb, rgb)
                t = False
                break

        if t:
            turtle.setposition(g * c.real, g * c.imag)
            turtle.dot(2, "black")

    turtle.update()

print("Calculated!")

turtle.mainloop()

The significant change is the use of the combination of tracer() and update() to avoid visually plotting every dot for the user and just drawing as each vertical column completes.

How I can make my Mandelbrot plotter faster?

1 Answers