Writing a mandelbrot set to an image in python

Question

I am trying to write a mandelbrot set to an image in python, and am having a problem with one of my functions.

The issue is: While I expect something like this. I am getting a plain white image. Here is my code:

Quick Summary of code: Check if value is in set, if it is, mark it as true in an array of booleans. Then, draw the image based on the array of booleans, coloring the true, and leaving the false ones.

import math
import numpy as np
import scipy.misc as smp
from PIL import PILLOW_VERSION
from PIL import Image

def iterate(x, y, iterationNum):
    z = 0
    coord = complex(x, y)
    for a in xrange(iterationNum):
        #Don't use fabs. It can be negative.
        z = z * z + coord
        #This is a comparison between complex and int. It probably won't work.
        #You want |Z| which is: z.real ** 2 + z.imag ** 2 > 4
        if math.fabs(z) > 2:
            return False
    return True

def pixel(image,x,y,r,g,b):
   """Place pixel at pos=(x,y) on image, with color=(r,g,b)"""
   image.put("#%02x%02x%02x" % (r,g,b), (y, x))

#here's some example coloring code that may help:
def draw(grid):
    #Create a white image with the size of the grid as the number of pixels
    img = Image.new('RGB', (len(grid), len(grid)), "white")
    pixels = img.load()
    for row in xrange(len(grid)):
        for col in xrange(len(grid[row])):
            if grid[row][col] == True:
                #If that point is True (it's in the set), color it blue
                pixels[row, col] = (0, 0, 255)
    return img

def mandelbrot():
    #you should probably use a square, it's easier to deal with
    #The mandelbrot set fits completely within (-2, 2) and (2, -2)
    #(-200, 200), (200, -200) is way too big!
    TopLeftX = -2; BottomRightX = 2
    TopLeftY = 2; BottomRightY = -2
    #increment should be calculated based on the size of the bounds and the number of pixels
    #For example, if you're between -2 and 2 on the X-Plane, and your image is 400 pixels wide
    #Then your increment = (2 - (-2)) / 400 = 4 / 400 = .01 so that each pixel is 1/400th of the
    #Total width of the bounding area
    increment = 0.01
    maxIt = 100
    w = BottomRightX - TopLeftX
    h = TopLeftY - BottomRightY
    #This should be based on the size of the image, one spot in the area for one pixel
    npArr = np.zeros((w / increment, h / increment), dtype=bool)
    #Use the increment variable from above. It won't work with xrange because that doesn't
    #Support decimals. You probably want to use a while loop or something
    x = -2
    y = 2
    while TopLeftX <= x <= BottomRightX:
        while TopLeftY <= y <= BottomRightY:
            #I recommend using True or False in here (in the set or not)
            #And then do your color calculations as I explained above
            #Saves a lot of memory
            if iterate(x, y, maxIt):
                npArr[x, y] = True
            y += increment
    #once you've calculated the Trues and Falses, you'd call the draw() function
    #using the npArr as the parameter. I haven't tested the code, so there may
    #be a few bugs, but it should be helpful!
        x += increment
    return npArr

img = draw(mandelbrot())
img.save("mandelbrot.png")

I suspect the problem is with the "iterate" function in my code, because none of the values i put in iterate are returning true.

EDIT I have another issue as well, The second for loop I have here isnt even running.

For any "truthy" value of `iterationNum`, `iteration` can't possibly return `True`, since it has an infinite loop that only contains a `return False`. Did you mean to do some sort of `for` loop or maybe change the value of `iterationNum` in the loop? — user94559, Sep 25 '16 at 06:44
Looks like you always pass `100` into `iteration`, so it can indeed only possibly return `False`. — user94559, Sep 25 '16 at 06:44
@smarx So do you think I should start at 1, and the iterate up to 100? — Arvind Ganesh, Sep 25 '16 at 06:48
I have no idea what you wanted to do. :-) You wrote the code... what did you want to happen? — user94559, Sep 25 '16 at 06:49
@smarx I have some pseudo code, if that might help. https://gist.github.com/AlexEKoren/e2a60b1b272049967057022a956dbe9b — Arvind Ganesh, Sep 25 '16 at 06:51
If `repeat numberOfIterations` means "do this thing `numberOfIterations` times", then you probably want `for _ in range(iterationNum):`. — user94559, Sep 25 '16 at 06:52

score 0 · Accepted Answer · answered Sep 25 '16 at 17:39

Your handling of the y coordinate is faulty. You begin the outer loop with

y = 2

and have the loop condition as

while TopLeftY <= y <= BottomRightY:

After substituting their values, this is

while 2 <= y <= -2:

which is a nonsense. This is followed by

y += increment

but y is already at the top end of the range. Moreover, you fail to reset y for each inner loop.

To summarise, the loop should be

x = TopLeftX                                # use the value you already defined!
while TopLeftX <= x <= BottomRightX:
    y = TopLeftY                            # moved to inside x loop
    while TopLeftY >= y >= BottomRightY:    # change the loop condition
        # ... the Mandelbrot iteration
        y -= increment                      # reverse direction
    x += increment

I am no Python expert, so there may be other problems too.

Thank you so much for the answer! I already fixed all the issues you pointed out, but I will makr yours as the right answer. Thanks! :D — Arvind Ganesh, Sep 25 '16 at 18:18

Writing a mandelbrot set to an image in python

1 Answers1