3d-visualization.py

"""

available mode : Lorenz : Edward Lorenz's famous butterfly attractor
                 Bouali : http://chaos-3d.e-monsite.com/medias/files/nody2.pdf
                 Arneodo : requires some adjustement with dt and iterations
                 Den Tsucs 


nb : parameter rho, beta, and sigma of Lorenz attractor can be modified in NextStep function
"""





startingPosition = [0.1, 0.1, 0.1] #starting point position
iterations = 1000000 #number of points to compute
mode = "Lorenz" #mode : available : "default"  "Bouali"  "Lorenz"  "Arneodo"  "Den Tsucs"
_LINEWIDTH = 0.05 #lower than 1 makes it transparent
_DISPLAY_EVOLUTION = True #If set to True, will plot X, Y, and Z on a plot at the end
start_display = 0
end_display = 50000

print(f'***** Current Settings ***** \n Starting Position =   {startingPosition}  \n Iterations = {iterations}  \n Mode = {mode} \n Settings can be updated directly in the file')




import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
from matplotlib import cm


axe = plt.figure().add_subplot(projection='3d')






def NextStep(pos, mode="default"):
    
    px = pos[0]
    py = pos[1]
    pz = pos[2]
        
    
    
    
    
    if mode == "Bouali":
        a = 4
        alpha = 0.3
        b = 1
        c = 1.5
        beta = 0.05
        s = 1
        
        x = px*(a-py) + alpha * pz
        y = -py*(b-px*px)
        z = -px*(c-s*pz) - beta*pz
        return x, y, z
    
    elif mode == "Lorenz":
        rho = 28
        sigma = 10
        beta = 8/3

        x = sigma * (py - px)
        y = px * (rho - pz) - py
        z = px*py - beta * pz

        return x, y, z

    elif mode == "Arneodo":
        a = 5.5
        b = 3.5
        c = 0.01

        x = py
        y = pz
        z = a*px -  b*py - pz - c*px*px*px

        return x, y, z

    elif mode == "Den Tsucs":
        a = 40
        c = 0.833
        d = 0.5
        e = 0.65
        f = 20

        x = a * (py - px) + d * px *pz
        y = f * py - px*pz
        z = c*pz + px*py - e * px *px

        return x, y, z













X = [startingPosition[0]]
Y = [startingPosition[1]]
Z = [startingPosition[2]]

sx, sy, sz = startingPosition[0], startingPosition[1], startingPosition[2]



for i in range(iterations):

    if(i%100000 == 0): print(i, "   ", i/iterations*100, "%")

    dt = 0.001

    ax, ay, az = NextStep([sx, sy, sz], mode)
    
    sx+=ax * dt
    sy+=ay * dt
    sz+=az * dt
    
    X.append(sx)
    Y.append(sy)
    Z.append(sz)

print("rendering")
axe.plot(X, Y, Z, marker="", linewidth=_LINEWIDTH)
plt.show()


if _DISPLAY_EVOLUTION:
    plt.plot(X[start_display:end_display], label="X")
    plt.plot(Y[start_display:end_display], label="Y")
    plt.plot(Z[start_display:end_display], label="Z")
    plt.title("Evolutions")
    plt.legend()
    plt.show()