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--- fractal [2011/04/12 23:45] – [Mandelbrot] cedric
+++ fractal [2011/04/12 23:47] – cedric
@@ Line 8: / Line 8: @@
 ====== Iterated function system ======
+In mathematics, [[http://en.wikipedia.org/wiki/Iterated_function_system | iterated function systems]] or IFSs are a method of constructing fractals; the resulting constructions are always self-similar.
 {{:barnsley-1.png|}}
@@ Line 143: / Line 145: @@
 {{:mandelbrot-python.png|}}
+<code python>
+try:
+    import Numeric as nm
+except:
+    print "program requires the Numeric module"
+    print "from --> http://numeric.scipy.org/"
+    raise SystemExit
+import Tkinter as tk
+import Image # PIL
+import ImageTk # PIL
+# set width and height of window
+#w ,h = 640, 600
+#w ,h = 1280, 1200
+w ,h = 2200, 2000
+#w ,h = 2560, 2400
+class Mandelbrot(object):
+    def __init__(self):
+        """
+        Create window
+        """
+        self.root = tk.Tk()
+        self.root.title("Mandelbrot Set")
+        self.create_image()
+        self.create_label()
+        # start event loop
+        self.root.mainloop()
+    def draw(self, x1, x2, y1, y2, maxiter=30):
+        """
+        Draw the Mandelbrot set.
+        """
+        xx = nm.arange(x1, x2, (x2-x1)/w*2)
+        yy = nm.arange(y2, y1, (y1-y2)/h*2) * 1j
+        q = nm.ravel(xx+yy[:, nm.NewAxis])
+        z = nm.zeros(q.shape, nm.Complex)
+        output = nm.resize(nm.array(0,), q.shape)
+        for iter in range(maxiter):
+            z = z*z + q
+            done = nm.greater(abs(z), 2.0)
+            q = nm.where(done,0+0j, q)
+            z = nm.where(done,0+0j, z)
+            output = nm.where(done, iter, output)
+        output = (output + (256*output) + (256**2)*output) * 8
+        # convert output to a string
+        self.mandel = output.tostring()
+    def create_image(self):
+        """"
+        Create the image from the draw() string
+        """
+        self.im = Image.new("RGB", (w/2, h/2))
+        # you can experiment with these x and y ranges
+        self.draw(-2.13, 0.77, -1.3, 1.3)
+        self.im.fromstring(self.mandel, "raw", "RGBX", 0, -1)
+    def create_label(self):
+        """
+        Put the image on a label widget
+        """
+        self.image = ImageTk.PhotoImage(self.im)
+        self.label = tk.Label(self.root, image=self.image)
+        self.label.pack()
+if __name__ == '__main__':
+    test = Mandelbrot()
+</code>