You can do it by plotting your variable as a function of the “natural” variable that parametrizes your curve. For example:
n = 12
a = np.arange(n)
x = 2**a
y = np.random.rand(n)
fig = plt.figure(1, figsize=(7,7))
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
ax1.plot(x,y)
ax1.xaxis.set_ticks(x)
ax2.plot(a, y) #we plot y as a function of a, which parametrizes x
ax2.xaxis.set_ticks(a) #set the ticks to be a
ax2.xaxis.set_ticklabels(x) # change the ticks' names to x
which produces:
