Mandelbrot Set Fractal

Question

I thought I would give this months community challenge a try. This is my first time using Python. It does take quite a while to run and it's not very colourful but it works.

from PIL import Image, ImageDraw
img = Image.new("RGB", (2400, 2400), "white")
draw = ImageDraw.Draw(img)
max_count = 200
width = img.size[0]
height = img.size[1]
for row in range(height):
 for col in range(width):
 str_output = ""
 c = complex(
 (col - float(width)/2.0)*5.0/float(width),
 (row - float(height)/2.0)*5.0/float(height)
 )
 iteration = 0
 z = 0
 while abs(z) < 2 and iteration < max_count:
 z = z**2 + c
 iteration += 1
 if abs(z) < 2:
 draw.point((col, row), fill="black")
 else:
 draw.point((col, row), fill=(255 - iteration,255 - iteration,255 - iteration))
img.save('mandelbrot.png')

black and white mandelbrot set

• SuperBiasedMan: What version of Python are you using?
• James Fenwick: @SuperBiasedMan 3.whatever_the_latest_release_is
• Justin: @JamesFenwick That would be 3.5

Answer 1

Your constants should be in UPPER_SNAKE_CASE

MAX_COUNT = 200
WIDTH = img.size[0]
HEIGHT = img.size[1]

Instead of nested for loops, you can use itertools.product which basically will perform the nested iteration you need:

from itertools import product
for row, col in product(range(height), range(width))

You don't use str_output, you should clean up unused values.

You should have whitespace either side of your mathematical operators and have a space after each comma in a comma separated list of values:

(col - float(width) / 2.0) * 5.0 / float(width),
draw.point((col, row), fill=(255 - iteration, 255 - iteration, 255 - iteration))

You should also keep lines below 79 characters as the Python style guide dictates. You can split lines quite easily when they're in paretheses:

 draw.point((col, row), fill=(255 - iteration, 255 - iteration,
 255 - iteration))

Also your mileage may vary on whether or not this is more readable but you could use a ternary for your final if condition. Like this:

 draw.point((col, row), fill=("black" if abs(z) < 2 else 
 (255 - iteration, 255 - iteration,
 255 - iteration))

The formatting is definitely more awkward, but I personally like these structures because it makes it clear that the only difference in the two results is that one condition.

Answer 2

• This feels a bit backwards to me

  img = Image.new("RGB", (2400, 2400), "white")
  width = img.size[0]
  height = img.size[1]
  

  compared to this

  WIDTH = 2400
  HEIGHT = 2400
  img = Image.new("RGB", (WIDTH, HEIGHT), "white")
  

• You can eliminate all the float calls because you are using Python 3 where true division is the default.

• for loops are generally preferred over while loops. A possible way to arrange the inner loop is this:

  z = 0
  for iteration in range(MAX_COUNT):
   z = z**2 + c
   if abs(z) >= 2:
   fill = (255 - iteration, 255 - iteration, 255 - iteration)
   break
  else:
   fill="black"
  draw.point((col, row), fill=fill)