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--- fractal [2011/04/12 23:47] – cedric
+++ fractal [2016/10/30 21:09] (current) – removed cedric
@@ Line 1: / Line 1: @@
-====== Fractal landscape ======
-Surface generated using a stochastic algorithm was my speciality when I studied fractals.
-A rapport and a presentation about landscape fractals (in french).
-{{:rapportir.pdf|}}
-{{:presentationir.pdf|}}
-====== 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|}}
-You can download the source code above: hg clone [[https://bitbucket.org/cedricbonhomme/iterated-function-system | https://bitbucket.org/cedricbonhomme/iterated-function-system]]
-<code ocaml>
-#load "graphics.cma";;
-type point = { x: float; y: float}
-type transfo = { pb: float; kf: float array}
-type ifs = { po: point; sz: point; lt: transfo list}
-let image kf p =
-    { x= kf.(0)*.p.x+.kf.(1)*.p.y+.kf.(2);
-    y= kf.(3)*.p.x+.kf.(4)*.p.y+.kf.(5)};;
-let rec choix_image p rd = function
-    | t::_ when rd<=t.pb -> image t.kf p
-    | _::lt -> choix_image p rd lt
-    | [] -> raise Not_found;;
-open Graphics;;
-open_graph " 400x640";;
-let pixel_of_point po sz p =
-    (int_of_float((p.x-.po.x)/.sz.x*.float_of_int(size_x())),
-    int_of_float((p.y-.po.y)/.sz.y*.float_of_int(size_x())));;
-let tracer fs n =
- let _ = clear_graph () in
-  let rec urs pt = function
-   | 0 -> ()
-   | i -> let p' = (choix_image pt (Random.float 1.0) fs.lt) in
-           let (xx,yy) = pixel_of_point fs.po fs.sz p' in
-            let _ = plot xx yy
-             in urs p' (i-1)
-  in urs {x= 1.0; y= 1.0} n;;
-let bizarre =
-{ po = {x= -2.25 ; y= -0.50};
-sz = {x= 5.00 ; y= 11.00};
-lt = [{pb= 0.84; kf= [| 0.85; 0.04; 0.00; -0.04; 0.85; 1.60|]};
-{pb= 0.91; kf= [|-0.15; 0.28; 0.00; 0.26; 0.24; 0.44|]};
-{pb= 0.98; kf= [| 0.20;-0.26; 0.00; 0.23; 0.22; 1.60|]};
-{pb= 1.00; kf= [| 0.00; 0.00; 0.00; 0.00; 0.16; 0.00|]}]};;
-let sierpinski =
-{ po = {x= -5.0 ; y= -8.0};
-sz = {x= 5.0 ; y= 3.0};
-lt = [{pb= 0.333; kf= [|0.5; 0.0; 0.0; 0.5; 0.0; 0.0|]};
-{pb= 0.666; kf= [|0.5; 0.0; 0.0; 0.5; 1.0; 0.0|]};
-{pb= 1.00; kf= [|0.5; 0.0; 0.0; 0.5; 0.5; 0.8660254|]}]};;
-let dragon =
-{ po = {x= -40.0 ; y= -10.0};
-sz = {x= 110.0 ; y= 110.0};
-lt = [{pb= 0.787473; kf= [| 0.824074; 0.281482; -10.88229; -0.212346;
-.864198; -0.110607|]};
-{pb= 1.0; kf= [| 0.288272; 0.720988; 0.78536; -0.463889; -0.377778;
-.095795|]}]};;
-let corail =
-{ po = {x= -45.0 ; y= -5.0};
-sz = {x= 95.0 ; y= 100.0};
-lt = [{pb= 0.40; kf= [| 0.307692; -0.531469; 50.401953; -0.461538;
--0.293706; 80.655175|]};
-{pb= 0.55; kf= [| 0.307692; -0.076923; -10.295248; 0.153846;
--0.447552; 40.152990|]};
-{pb= 1.00; kf= [| 0.000000; 0.545455; -40.893637; 0.692308;
--0.195804; 70.269794|]}]};;
-let arbre =
-{ po = {x= -0.3 ; y= 0.0};
-sz = {x= 0.6 ; y= 0.5};
-lt = [{pb= 0.05; kf= [| 0.0; 0.0; 0.0; 0.0; 0.5; 0.0|]};
-{pb= 0.45; kf= [| 0.42; -0.42; 0.0; 0.42; 0.42; 0.2|]};
-{pb= 0.85; kf= [| 0.42; 0.42; 0.0; -0.42; 0.42; 0.2|]};
-{pb= 1.00; kf= [| 0.1; 0.0; 0.0; 0.0; 0.1; 0.2|]}]};;
-let etoile =
-{ po = {x= -50.0 ; y= -20.0};
-sz = {x= 100.0 ; y= 100.0};
-lt = [{pb= 0.912675; kf= [| 0.745455; -0.459091; 10.460279; 0.406061;
-.887121; 0.691072|]};
-{pb= 1.0; kf= [| -0.424242; -0.065152; 30.809567; -0.175758;
--0.218182; 60.741476|]}]};;
-let zigzag =
-{ po = {x= -70.0 ; y= -20.0};
-sz = {x= 150.0 ; y= 130.0};
-lt = [{pb= 0.888128; kf= [| -0.632407; -0.614815; 30.840822;
--0.54537;
-.659259; 10.282321|]};
-{pb= 1.0; kf= [| -0.036111; 0.444444; 20.071081; 0.210185; 0.037037;
-.330552|]}]};;
-let cristal =
-{ po = {x= -0.0 ; y= -70.0};
-sz = {x= 100.0 ; y= 140.0};
-lt = [{pb= 0.747826; kf= [| 0.69697; -0.481061; 20.147003; -0.393939;
--0.662879; 10.310288|]};
-{pb= 1.0; kf= [| 0.090909; -0.443182; 40.286558; 0.515152; -0.094697;
-.925762|]}]};;
-let binary =
-{ po = {x= -50.0 ; y= -1.0};
-sz = {x= 100.0 ; y= 95.0};
-lt = [{pb= 0.333333; kf= [| 0.5; 0.0; -20.563477; 0.0; 0.5;
--0.000003|]};
-{pb= 0.666666; kf= [| 0.5; 0.0; 20.436544; 0.0; 0.5; -0.000003|]};
-{pb= 1.0; kf= [| 0.0; -0.5; 40.873085; 0.5; 0.0; 70.563492|]}]};;
-let galaxie =
-{ po = {x= -8.0 ; y= -1.0};
-sz = {x= 16.0 ; y= 12.0};
-lt = [{pb= 0.787879; kf= [| 0.787879; -0.424242; 1.758647; 0.242424;
-.859848; 1.408065|]};
-{pb= 0.909091; kf= [| -0.121212; 0.257576; -6.721654; 0.151515;
-.053030; 1.377236|]};
-{pb= 1.0; kf= [| 0.181818; -0.136364; 6.086107; 0.090909; 0.181818;
-.568035|]}]};;
-let koch =
-{ po = {x= -2.25 ; y= -4.0};
-sz = {x= 11.00 ; y= 8.00};
-lt = [{pb= 0.25; kf= [|0.333; 0.0; 0.0; 0.333; 0.0; 0.0|]};
-{pb= 0.50; kf= [|0.167; -0.287; 0.287; 0.167; 0.333; 0.0|]};
-{pb= 0.75; kf= [|0.167; 0.287; -0.287; 0.167; 0.5; 0.287|]};
-{pb= 1.0; kf= [|0.333; 0.0; 0.0; 0.333; 0.667; 0.0|]}]};;
-</code>
-====== Mandelbrot ======
-{{: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>