Beleg_Mandelbrotmenge v1.0

Version 1.0
log
- Zeichnungsfunktion wird realisiert
- Größe der 'canvas' wird auf 400*400 einstellt

Beleg_Mandelbrotmenge.py

@@ -0,0 +1,91 @@
+# 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):
+
+    xscale = float(canvas["width"]) / (Xmax - Xmin)                             # Calculate the x axis zoom scale of canvas width and range of real part of c
+    yscale = float(canvas["height"]) / (Ymax - Ymin)                            # Calculate the y axis zoom scale of canvas height and range of imaginary part of c
+    xstep = (Xmax - Xmin) / (float(canvas["width"]))                            # Calculate the changing step im x axis
+    ystep = (Ymax - Ymin) / (float(canvas["height"]))                           # 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 the squares of every single pixels with side length 1 and selected color
+                                    (x - Xmin)*xscale, (y - Ymin)*yscale,       # The positions have been also multiplied by the zoom scale so it can fit to the
+                                    fill=color, outline = color)                # canvas when it has been changed
+            y += ystep
+        x += 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 so 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 -2
+Xmax = 0.5                                                                      # The maxmimum of real part set 0.5
+Ymin = -1                                                                       # The minimum of imaginary part set -1
+Ymax = 1                                                                        # The maximum of imaginary part set 1
+
+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=400, height=400, bg="white")                        # The size and background of the window has been set
+canvas.pack()                                                                   # The window will be showed
+
+Mandelbrot(Xmin, Xmax, Ymin, Ymax)                                              # The color of every pixel in the canvas has been calculated with help of the Mandelbrot funktion
+
+root.mainloop()