Example use of symlog (symmetric log) axis scaling.
import matplotlib.pyplot as plt
import numpy as np
dt = 0.01
x = np.arange(-50.0, 50.0, dt)
y = np.arange(0, 100.0, dt)
plt.subplot(311)
plt.plot(x, y)
plt.xscale('symlog')
plt.ylabel('symlogx')
plt.grid(True)
plt.gca().xaxis.grid(True, which='minor') # minor grid on too
plt.subplot(312)
plt.plot(y, x)
plt.yscale('symlog')
plt.ylabel('symlogy')
plt.subplot(313)
plt.plot(x, np.sin(x / 3.0))
plt.xscale('symlog')
plt.yscale('symlog', linthreshy=0.015)
plt.grid(True)
plt.ylabel('symlog both')
plt.tight_layout()
plt.show()