Computer Programming 150

(April 28, 2008)

The Mandelbrot Set

1. Mandelbrot.py

#

# Name: Mandelbrot.py

# Date: April 27, 2008

#

from graphics import *

from math import *

from button import *

class Grid401:

#

# 401 x 401 pixel window

#

def __init__(self, win, xmin, ymin, xmax, ymax):

self.CP_x = 0

self.CP_y = 0

self.CD = 0.0

self.color = "black"

self.p1 = Point(39, 441) # lower left

self.p2 = Point(441, 39) # upper right

self.grid = win

self.grid.setBackground("white")

#

# world to screen coefficients

#

self.A = 400.0 / (xmax – xmin)

self.B = -400.0 * xmin / (xmax - xmin)

self.C = 400.0 / (ymax - ymin)

self.D = -400.0 * ymin /(ymax - ymin)

def clear(self):

#

# Clear window

#

window = Rectangle(self.p1, self.p2)

window.setFill("white")

window.draw(self.grid)

def setPixel(self, x0, y0):

#

# Set pixel at world coordinates x0, y0

#

x = self.A * x0 + self.B

y = self.C * y0 + self.D

self.grid.plotPixel(40+x, 440-y, self.color)

def update(self, xmin, ymin, xmax, ymax):

#

# update world to screen transformation coefficients

#

self.A = 400.0 / (xmax - xmin)

self.B = -400.0 * xmin / (xmax - xmin)

self.C = 400.0 / (ymax - ymin)

self.D = -400.0 * ymin /(ymax - ymin)

def drawLine(self, x0, y0, x1, y1):

#

# draws line given world coordinates

#

x0 = self.A * x0 + self.B

y0 = self.C * y0 + self.D

x1 = self.A * x1 + self.B

y1 = self.C * y1 + self.D

line = Line(Point(40+x0, 40+y0), Point(40+x1,40+y1))

line.setOutline(self.color) # current color

line.draw(self.grid)

def setColor3i(self, r, g, b):

self.color = color_rgb(r, g, b)

def setColor(self, color):

self.color = color

def main():

screenWidth = 640

screenHeight = 480

win = GraphWin("The Mandelbrot Set" , screenWidth, screenHeight) # window size

win.setCoords(0, 0, screenWidth, screenHeight)

# initial world coordinates for Mandelbrot set

xmin, ymin = -2.25, -1.5

xmax, ymax = 0.75, 1.5

# create the Grid401 object

myGrid = Grid401(win, xmin, ymin ,xmax, ymax)

# create and activate buttons

quitButton = button(win, Point(500, 50), 80, 20, " QUIT ")

clearButton = button(win, Point(500, 80), 80, 20, " CLEAR ")

drawButton = button(win , Point(500, 110), 80, 20, " DRAW ")

resetButton = button(win, Point(500, 140), 80, 20, "RESET")

quitButton.activate()

clearButton.activate()

drawButton.activate()

resetButton.activate()

myGrid.clear()

# event handling loop

while (True):

p = win.getMouse()

# check for zoom point

if (40 < p.getX() < 440) and (40 < p.getY() < 440):

xLength = xmax - xmin

yLength = ymax - ymin

xCenter = xmin + ((p.getX()-40)/400.0) * (xmax - xmin)

yCenter = ymin + ((p.getY()-40)/400.0) * (ymax - ymin)

xmin, xmax = xCenter - xLength/4.0, xCenter + xLength/4.0

ymin, ymax = yCenter - yLength/4.0, yCenter + yLength/4.0

myGrid.update(xmin, ymin, xmax, ymax)

# reset to original world coordinates

elif resetButton.clicked(p):

xmin, ymin = -2.25, -1.5

xmax, ymax = 0.75, 1.5

myGrid.update(xmin, ymin, xmax, ymax)

# draw Mandelbrot set – using escape algorithm

elif drawButton.clicked(p):

deltaX = (xmax - xmin)/400.0

deltaY = (ymax - ymin)/400.0

for j in range(401):

for i in range(401):

c = complex(xmin + i*deltaX, ymin + j*deltaY)

z = complex(0.0, 0.0)

for k in range(201):

z = z*z + c

if abs(z) >= 2:

break;

if k == 200:

myGrid.setColor("black")

elif (0 <= k < 20):

myGrid.setColor("red")

elif (0 <= k < 40):

myGrid.setColor("darkred")

elif (40 <= k < 60):

myGrid.setColor("orange")

elif (60 <= k < 80):

myGrid.setColor("brown")

elif (80 <= k < 100):

myGrid.setColor("yellow")

elif (100 <= k < 120):

myGrid.setColor("green")

elif (120 <= k < 140):

myGrid.setColor("cyan")

elif (140 <= k <= 160):

myGrid.setColor("blue")

elif (160 <= k < 180):

myGrid.setColor("violet")

elif (180 <= k < 200):

myGrid.setColor("magenta")

else:

myGrid.setColor("black")

myGrid.setPixel(c.real, c.imag)

elif clearButton.clicked(p):

myGrid.clear()

elif quitButton.clicked(p):

break

win.close()

main()