Generates and renders the Mandelbrot Set using the matplotlib library

gistfile1.py

from pylab import *
from math import log
from Tkinter import Tk
from tkFileDialog import *
import csv

H = 500
iterations = 30
ColorList = []

#Majority of processing work completed here.
#Calculates how close a point is to the mandelbrot set
def mandelbrot(real, imag):
    #z = complex(-0.726895347709114071439, 0.188887129043845954792)
    z = complex(0,0)
    c = complex(real, imag)
    dropOutLevel = 0
    for i in range(0, iterations):
        if abs(z) < 2:
            z = z**2 + c
            dropOutLevel += 1
        else:
            break

    z = z**2 + c
    z = z**2 + c
    z = z**2 + c
    z = z**2 + c
    return dropOutLevel,z

#Interpolates (Smooths) between 2 different colours
def interpolateC(color,endColor,left):
    if left == 0:
        return color
    rStart = color[0]
    gStart = color[1]
    bStart = color[2]
    rEnd = endColor[0]
    gEnd = endColor[1]
    bEnd = endColor[2]
    rDiff = rEnd-rStart
    gDiff = gEnd-gStart
    bDiff = bEnd-bStart
    rInc = float(rDiff)/left
    gInc = float(gDiff)/left
    bInc = float(bDiff)/left
    #print (str(left))
    return [rStart+rInc,gStart+gInc,bStart+bInc]

#Reads colour stops from a file chosen by the user using the tkinter library
def getPoints():
    Tk().withdraw() # we don't want a full GUI, so keep the root window from appearing
    filename = askopenfilename() # show an "Open" dialog box and return the path to the selected file
    reader = csv.reader(open(filename, "rb"), delimiter=',')
    pointsList = []
    for row in reader:
        colorList = []
        for a in row:
            colorList.append(float(a)/255)
        pointsList.append(colorList)

    backwards = pointsList[0:-1]
    backwards.reverse()
    return pointsList+backwards

#Gets the location to save the file
def getSaveLocation():
    Tk().withdraw()
    savefile = asksaveasfilename(defaultextension='.png')
    return savefile

#Sets up a list of colours for the rendering to use from the points file
def colorList():
    cols = []
    points = getPoints()
    eachLength = H/(len(points)-1)
    howmanytogo = eachLength
    
    for a in range(1,len(points)):
        cols.append(points[a-1])
        for i in range (0,eachLength):
            cols.append(interpolateC(cols[-1],points[a],howmanytogo))
            howmanytogo += -1


        howmanytogo = eachLength
    global ColorList
    ColorList = cols

#Turns a number from v() into a colour for the renderer to display
def toColor(a):
    a=a*85
    a = int(a)%H
    try:
        return ColorList[int(a)]
    except IndexError:
        print a
        print len(ColorList)
        return ColorList[0]

#Smooths the numbers from mandelbrot() to create an even gradient
def v(z,n):
    try:
        x = n + 1 - log2(log2(abs(z)))/log2(2)
        return x
    except ValueError:
        print(str(z))
    return 0

#Initialise, get inputs
colorList()
saveFile = getSaveLocation()
wDensity = int(raw_input("What width?"))
hDensity = int(raw_input("What height?"))
x_ords = []
y_ords = []
colors = []
left = float(raw_input("What is the leftmost value? "))
right = float(raw_input("What is the rightmost value? "))
bottom = float(raw_input("What is the bottommost value? "))
top = float(raw_input("What is the topmost value? "))
print "Calculating... "
w = right - left
h = top - bottom
wGap = w/wDensity
hGap = h/hDensity
wPercentageGap = w/100
a = left
perc = 0
print "0%"
#Calculate for each value and add to a list for rendering
while a < right:
    b = bottom
    while b < top:
        x_ords.append(a)
        y_ords.append(b)
        n, z = mandelbrot(a,b)
        if (n == iterations):
            col = [0.0,0.0,0.0]
        else:
            col = toColor(v(z,n))
        #print col
        colors.append(col)
        b += hGap
    a += wGap
    #Print percentage
    curPerc = ((right-a)/w) * 100
    if curPerc > perc+10:
        perc += 10
        print str(perc),"%"
    if curPerc > perc+5:
        perc += 5
        print str(perc),"%"

#render and save the image
print "Rendering... "
autoscale(tight=True)
scatter(x_ords, y_ords, s=1, c=colors, linewidths=0)
F = gcf()
F.set_size_inches(wDensity/80,hDensity/80)
F.savefig(saveFile)