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- # Programmierung 2 Beleg
- # Aufgabe 6
- # Mandelbrotmenge
- # Yuan Chen MAB14 4060920
- #--------------------------------------------------------------------------
- # Import module
- from tkinter import * # All modules of TKinter have been imported
- #--------------------------------------------------------------------------
- # Create a funktion that draw the rectangles with selected color of the
- # every single pixels in the canvas
- def Mandelbrot(Xmin, Xmax, Ymin, Ymax, lenth, pointssize):
- xscale = lenth / (Xmax - Xmin) # Calculate the x axis zoom scale of canvas width and range of real part of c
- yscale = lenth / (Ymax - Ymin) # Calculate the y axis zoom scale of canvas height and range of imaginary part of c
- xstep = (Xmax - Xmin) / lenth # Calculate the changing step im x axis
- ystep = (Ymax - Ymin) / lenth # Calculate the changing step im y axis
- x = Xmin # x change from the inputed minimum value Xmin to the inputed maximum value Xmax
- while x < Xmax:
- y = Ymin # y change from the inputed minimum value Ymin to the inputed maximum value Ymax
- while y < Ymax:
- c = c_count(complex(x, y)) # Read c for the current x and y with help of the c_count funktion
- if c == i_limit: # Judge if c is equal to the limit which in this case 20
- color = "red" # If ture give it the color red
- else:
- color = colorlist[c] # If not give it the color with help of the getColor funktion
- canvas.create_rectangle((x - Xmin)*xscale, (y - Ymin)*yscale, # Draw a square for every single point
- (x - Xmin)*xscale + pointssize, # with pointssize 4
- (y - Ymin)*yscale + pointssize,
- fill=color,outline="black") # and with selected fillcolor from the colorlist and outline in black in this case (blue outline looks wierd)
- y += pointssize*ystep
- x += pointssize*xstep
- #--------------------------------------------------------------------------
- # Create a funktion that calculate the time of iterations with gived c and
- # the gived maximum absolute value of z_n+1 which is 2 in this case
- def c_count(c):
- z = complex(0,0) # Defined a complex number z with intial value (0,0)
- for ite in range(i_limit): # Time of iterations changes from 0 to the count limit which is 20 in this case
- z = z*z + c # The calculation fomula
- if abs(z) > 2: # Judge if the absolute value of z has exceeded 2
- return ite # If it is exceeded, return the time of iterations
- return i_limit # If not then return the limit
- #--------------------------------------------------------------------------
- # Create a funktion that add different colors to the setcolorlist for the
- # different section of time of iterations
- def getColor(iter):
- for iter in range(i_limit): # The time of iterations changes from 0 to the count limit.
- if iter < 3 : # If it's 0 - 2 (time of interations: 1 - 3), set the color as 'magenta'.
- colorlist.append('magenta')
- elif iter < 7 : # If it's 3 - 6 (time of interations: 4 - 7), set the color as 'blue' .
- colorlist.append('blue')
- elif iter < 11 : # If it's 7 - 10 (time of interations: 8 - 11), set the color as 'green'.
- colorlist.append('#00FF00') # I tried just 'green' but it showed dark green instead, so I used rgb color here therefor the right color can be showed
- elif iter < 15 : # If it's 11 - 14 (time of interations: 12 - 15), set the color as 'yellow'.
- colorlist.append('yellow')
- else : # If it's 15 or greater (time of interations: 16 or greater), set the color as 'red'.
- colorlist.append('red')
- #------------------------------------------------------------------------------
- # Main programm
- i_limit = 20 # The time of iterations will be limited within 20
- Xmin = -2.0 # The minimum of real part set as -2
- Xmax = 0.5 # The maxmimum of real part set as 0.5
- Ymin = -1 # The minimum of imaginary part set as -1
- Ymax = 1 # The maximum of imaginary part set as 1
- pointsamount = 100 # The amount of points in the both sides set as 100
- pointssize = 4 # The size of points set as 4
- lenth = pointsamount * pointssize # Set the width and the height of the canvas
- iter = 0 # Iterations has been initialized
- colorlist = [] # Colorlist has been initialized
- getColor(iter) # Colors has been added to the Colorlist with help of getColor funktion
- root = Tk() # The TK class has been initialized
- root.title("Mandelbrotmenge - By Yuan Chen") # The title has been set
- canvas = Canvas(root, width=lenth, height=lenth, bg="white") # The size and background of the window has been set
- canvas.pack() # The window will be showed
- Mandelbrot(Xmin, Xmax, Ymin, Ymax, lenth, pointssize) # The color of every point has been calculated and showed on th canvas with help of the Mandelbrot funktion
- root.update()
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