Python matplotlib adjust colormap

This is what I want to create.

This is what I get.

This is the code I have written.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm

x = np.linspace(-90, 90, 181)
y = np.linspace(-90, 90, 181)
x_grid, y_grid = np.meshgrid(x, y)
z = np.e**x_grid

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection="3d")
ax.plot_surface(x_grid, y_grid, z, cmap=cm.rainbow)

I also tried to normalize z and the colormap.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import cm
import matplotlib as mpl

x = np.linspace(-90, 90, 181)
y = np.linspace(-90, 90, 181)
x_grid, y_grid = np.meshgrid(x, y)
z = np.e**x_grid
cmap = mpl.cm.rainbow
norm = mpl.colors.Normalize(vmin=0, vmax=1)

fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection="3d")
ax.plot_surface(x_grid, y_grid, z/np.max(z), norm=norm, cmap=cm.rainbow)

Question: How can I adjust the colormap to make it less discrete and more continuous for these simultaneously tiny and large values in z?

Your problem is related to the fact that you are working with exponential numbers, but you're using a linear colormap. For x=90 you have z=1.2e+39, reaaaally large.

You were very close with your second attempt! I just changed 1 line in there, instead of

norm = mpl.colors.Normalize(vmin=0, vmax=1)

I used

norm = mpl.colors.LogNorm()

And the result I got was the following:

Now, you can tweak this as much as you like in order to get the colors you want :) Just don't forget that your colormap should be normalized in a logarithmic fashion, so that it counters the exponential behaviour of your function in this case.