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Lorenz Attractor

Python, 45 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45``` ```# Lorenz Attractor (projected onto XY-plane) # http://en.wikipedia.org/wiki/Lorenz_attractor # FB - 201107317 import random from PIL import Image imgx = 800 imgy = 600 image = Image.new("RGB", (imgx, imgy)) maxIt = 100000 # number of pixels to draw size = 30 xa = -size xb = size ya = -size yb = size # initial state x = random.random() * size * 2 - 1 y = random.random() * size * 2 - 1 z = random.random() * size * 2 - 1 # dx/dt = delta * (y - x) # dy/dt = r * x - y - x * z # dz/dt = x * y - b * z delta = float(10) # Prandtl number r = float(28) b = float(8) / 3 h = 1e-3 # time step def Lorenz(x, y, z): dx_dt = delta * (y - x) dy_dt = r * x - y - x * z dz_dt = x * y - b * z x += dx_dt * h y += dy_dt * h z += dz_dt * h return (x, y, z) for i in range(maxIt): (x, y, z) = Lorenz(x, y, z)#; print x, y, z xi = int((imgx - 1) * (x - xa) / (xb - xa)) yi = int((imgy - 1) * (y - ya) / (yb - ya)) if xi >=0 and xi < imgx and yi >= 0 and yi < imgy: image.putpixel((xi, yi), (255, 255, 255)) image.save("Lorenz_Attractor.png", "PNG") ```
 Created by FB36 on Sun, 31 Jul 2011 (MIT)