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 avoid all the float calls by putting this at the top, or by using Python 3:

  from __future__ import division

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)

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)

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 avoid all the float calls by putting this at the top, or by using Python 3:

  from __future__ import division

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 avoid all the float calls by putting this at the top, or by using Python 3:

  from __future__ import division

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)