forked from scienceetonnante/Chaos
-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy path12-lorenz_poly.py
113 lines (83 loc) · 3.26 KB
/
12-lorenz_poly.py
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
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
import numpy as np
import matplotlib.pyplot as plt
import scipy.integrate as integrate
import matplotlib.animation as animation
import mpl_toolkits.mplot3d.axes3d as p3
plt.rcParams['animation.ffmpeg_path'] = r'/Volumes/Data/Youtube/[ffmpeg]/ffmpeg'
FIGSIZE = (16,9)
DPI = 120 # 240 For 4K, 60 for 720p
T = 200
SUB_SAMPLING = 10
###############################################################################
''' Parameters & Differential equation '''
sigma = 10
rho = 28
beta = 8/3
def derivs(state, t):
x, y, z = state[0], state[1], state[2]
res = np.zeros_like(state)
res[0] = sigma * (y - x)
res[1] = x * (rho - z) - y
res[2] = x * y - beta * z
return res
###############################################################################
# Time range
dt = 0.01
t = np.arange(0.0, T, dt)
# initial state
#init_state_list = [[10, 10, 10],[-10,10,10],[10,-10,-10],[-10,-10,10]]
init_state_list = [[-5, 5, 5],[-5.001,5.001,5.001]] #,[10,10.001,10],[10,10,10.001]]
# integration
res_list = [integrate.odeint(derivs, init_state, t) for init_state in init_state_list]
###############################################################################
#fig = plt.figure(figsize=FIGSIZE,dpi=DPI)
#ax = fig.add_subplot(111, projection='3d')
#ax.view_init(elev=None, azim=None)
#ax.set_axis_bgcolor('black')
#ax.w_xaxis.set_pane_color((0,0,0,0))
#ax.w_yaxis.set_pane_color((0,0,0,0))
#ax.w_zaxis.set_pane_color((0,0,0,0))
#ax.set_xlim3d([-30, 30])
#ax.set_ylim3d([-30, 30])
#ax.set_zlim3d([-10, 50])
#
#lines = [plt.plot(res[:,0],res[:,1],res[:,2], '-', lw=1) for res in res_list]
###################################################################################
azim_start = -160.0
azim_end = 160.0
fig = plt.figure(figsize=FIGSIZE,dpi=DPI)
ax = p3.Axes3D(fig)
ax.set_axis_bgcolor('black')
ax.w_xaxis.set_pane_color((0,0,0,0))
ax.w_yaxis.set_pane_color((0,0,0,0))
ax.w_zaxis.set_pane_color((0,0,0,0))
ax.set_xlim3d([-30, 30])
ax.set_ylim3d([-30, 30])
ax.set_zlim3d([-10, 50])
ax.view_init(azim=azim_start)
lines = [ax.plot(res[:,0],res[:,1],res[:,2], '-', lw=1)[0] for res in res_list]
balls = [ax.plot(res[0:1,0],res[0:1,1],res[0:1,2], 'o', lw=1)[0] for res in res_list]
NB_FRAMES = int(np.floor(len(t)/SUB_SAMPLING))
def init():
for line, ball, res in zip(lines,balls, res_list):
x, y, z = res[:,0], res[:,1], res[:,2]
line.set_data([], [])
line.set_3d_properties([])
ball.set_data(x[0],y[0])
ball.set_3d_properties(z[0])
return lines, balls #, time_text
def animate(i, res_list, lines):
print("Computing frame",i)
ax.view_init(azim=azim_start+(azim_end-azim_start)*i/NB_FRAMES)
for line,res,ball in zip(lines,res_list,balls):
x, y, z = res[:,0], res[:,1], res[:,2]
line.set_data(x[:i*SUB_SAMPLING], y[:i*SUB_SAMPLING])
line.set_3d_properties(z[:i*SUB_SAMPLING])
ball.set_data(x[i*SUB_SAMPLING],y[i*SUB_SAMPLING])
ball.set_3d_properties(z[i*SUB_SAMPLING])
return lines, balls #, time_text
ani = animation.FuncAnimation(fig, animate, np.arange(0, NB_FRAMES), fargs=(res_list, lines), init_func = init,
interval=40, blit=False)
writer = animation.FFMpegWriter(fps=30, bitrate=5000)
ani.save('12-lorenz_poly.mp4', writer = writer, dpi=DPI)
plt.show()