Matplotlib-GIF-3D for Lorenz Systems

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import numpy as np,os

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from scipy import integrate

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from matplotlib import pyplot as pl,animation as an

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from mpl_toolkits.mplot3d import Axes3D

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N_trajectories=20

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def lorentz_deriv(params,t0,sigma=10.,beta=8./3,rho=28.):

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    x,y,z=params

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    return [sigma*(y-x),x*(rho-z)-y,x*y-beta*z]

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np.random.seed(1)

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x0=-15+30*np.random.random((N_trajectories,3))

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t=np.linspace(0,4,1000)

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x_t=np.asarray([integrate.odeint(lorentz_deriv,x0i,t) for x0i in x0])

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fig=pl.figure()

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ax=fig.add_axes([0,0,1,1],projection='3d'); ax.axis('off')

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colors=pl.cm.jet(np.linspace(0,1,N_trajectories))

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lines=sum([ax.plot([],[],[],'-',c=c) for c in colors],[])

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pts=sum([ax.plot([],[],[],'o',c=c) for c in colors],[])

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ax.set_xlim((-25,25)); ax.set_ylim((-35,35)); ax.set_zlim((5,55))

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ax.view_init(30,0)

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def init():

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    for line,pt in zip(lines,pts):

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        line.set_data([],[]); line.set_3d_properties([])

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        pt.set_data([],[]); pt.set_3d_properties([])

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    return lines+pts

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def animate(i):

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    i=(2*i)%x_t.shape[1]

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    for line, pt, xi in zip(lines,pts,x_t):

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        x,y,z=xi[:i].T

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        line.set_data(x,y); line.set_3d_properties(z)

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        pt.set_data(x[-1:],y[-1:]); pt.set_3d_properties(z[-1:])

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    ax.view_init(30,.3*i)

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    fig.canvas.draw()

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    return lines+pts

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anim=an.FuncAnimation(

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    fig,animate,frames=500,interval=30,blit=True,save_count=1500)

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f=r'animation.gif'

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writergif=an.PillowWriter(fps=15)

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anim.save(f,writer=writergif)

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fpath='https://sagecell.sagemath.org/kernel/'

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fpath+=os.getcwd()[14:]+'/files/'

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s1='<figure><embed type="image/gif" src="'

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s2='animation.gif" width=600/></figure>'

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html(s1+fpath+s2)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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