fractal
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Table of Contents
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
You can download the source code above: hg clone https://bitbucket.org/cedricbonhomme/iterated-function-system
#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; 0.864198; -0.110607|]}; {pb= 1.0; kf= [| 0.288272; 0.720988; 0.78536; -0.463889; -0.377778; 80.095795|]}]};; 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; 0.887121; 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; 0.659259; 10.282321|]}; {pb= 1.0; kf= [| -0.036111; 0.444444; 20.071081; 0.210185; 0.037037; 80.330552|]}]};; 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; 20.925762|]}]};; 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; 0.859848; 1.408065|]}; {pb= 0.909091; kf= [| -0.121212; 0.257576; -6.721654; 0.151515; 0.053030; 1.377236|]}; {pb= 1.0; kf= [| 0.181818; -0.136364; 6.086107; 0.090909; 0.181818; 1.568035|]}]};; 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|]}]};;
Mandelbrot
<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 = 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
fractal.1302643724.txt.gz ยท Last modified: 2011/04/12 23:28 by cedric