Amor Natura

import numpy as np

import matplotlib.pyplot as plt

def xftn(x, y):

return y

def yftn(x, y):

tmp = -x + y*(1-x*x)

return tmp

def xRK4(x, y, dt):

    k1 = dt * xftn(x, y)

    k2 = dt * xftn(x + 0.5*k1, y + 0.5*k1)

    k3 = dt * xftn(x + 0.5*k2, y + 0.5*k2)

    k4 = dt * xftn(x + k3, y + k3)

    result = x + k1 / 6 + k2 / 3 + k3 / 3 + k4 / 6

    return result

def yRK4(x, y, dt):

    k1 = dt * yftn(x, y)

    k2 = dt * yftn(x + 0.5*k1, y + 0.5*k1)

    k3 = dt * yftn(x + 0.5*k2, y + 0.5*k2)

    k4 = dt * yftn(x + k3, y + k3)

    result = y + k1 / 6 + k2 / 3 + k3 / 3 + k4 / 6

    return result

Step = 0.1

xLeft = -2

xRight = 2

yTop = 2

yBottom = -2

SIZE = (int)((xRight-xLeft)/Step) + 1  #We only think square plane.

print("Step is", Step)

x = np.empty((SIZE,SIZE), float)

y = np.empty((SIZE,SIZE), float)

u = np.empty((SIZE,SIZE), float)

v = np.empty((SIZE,SIZE), float)

for i in range(SIZE):

for j in range(SIZE):

x[i][j] = xLeft + Step*i

y[i][j] = yBottom + Step*j

u[i][j] = xftn(x[i][j], y[i][j])

v[i][j] = yftn(x[i][j], y[i][j])

xPointList = [0.5]

yPointList = [0.5]

timeList   = [0]

dt = 0.01

for i in range(1500):

xPointList.append(xRK4(xPointList[i], yPointList[i], dt))

yPointList.append(yRK4(xPointList[i], yPointList[i], dt))

timeList.append(timeList[i]+dt)

ax1 = plt.subplot2grid((7,3), (0,0), rowspan=5, colspan=5)

ax1.quiver(x,y,u,v, angles='xy', pivot='middle')

ax1.plot(xPointList, yPointList)

plt.xlim(-2, 2)

plt.ylim(-2, 2)

ax2 = plt.subplot2grid((7,3), (5,0), colspan=3)

ax2.plot(timeList, xPointList)

ax3 = plt.subplot2grid((7,3), (6,0), colspan=3)

ax3.plot(timeList, yPointList)

plt.show()

import matplotlib.pyplot as plt

import numpy as np

x = np.empty((10,10), float)

y = np.empty((10,10), float)

u = np.empty((10,10), float)

v = np.empty((10,10), float)

for i in range(10):

    for j in range(10):

        x[i][j] =  i / 10.0

        y[i][j] =  j / 10.0

        u[i][j] =  i / 10 * 2 

        v[i][j] =  j / 10 * 2

print(x, y, u, v)

plt.quiver(x,y,u,v, angles='xy', pivot='middle')

plt.ylim(0,1.1)

plt.xlim(0,1.1)

plt.grid('on')

plt.show()