Creating a modulo/folded plot in Python

Question

I am trying to "fold" an exponential plot (and a fit to it - see the first image below) around a discrete interval on the x-axis (a.k.a a "modulo plot"). The aim is that after 10 x-units the exponential is continued on the same plot from 0 for the 10 to 20 interval, as shown on a second "photoshopped" image below.

The MWE code is below:

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

Generate points

x=np.arange(20)
y=np.exp(-x/10)

Fit to data

def fit_func(x, t):
    return np.exp(-x/t)
par, pcov = optimize.curve_fit(f=fit_func, xdata=x, ydata=y)

Plot data and fit function

fig, ax = plt.subplots()
ax.plot(x,y, c='g', label="Data");
ax.plot(x,fit_func(x, par), c='r', linestyle=":", label="Fit");
ax.set_xlabel("x (modulo 10)")
ax.legend()
plt.savefig("fig/mod.png", dpi=300)

What I have: Origianl exponential from 0 to 20

What I want: Modulo/folded exponential in intervals of 10

Answer 1

You could try to simply write:

ax.plot(x % 10,y, c='g', label="Data")
ax.plot(x % 10, f, c='r', linestyle=":", label="Fit")

but then you get confusing lines connecting the last point of one section to the first point of the next.

Another idea is to create a loop to plot every part separately. To avoid multiple legend entries, only the first section sets a legend label.

import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt

x=np.arange(40)
y=np.exp(-x/10)
def fit_func(x, t):
    return np.exp(-x/t)

par, pcov = optimize.curve_fit(f=fit_func, xdata=x, ydata=y)
f = fit_func(x, par)
fig, ax = plt.subplots()

left = x.min()
section = 1
while left < x.max():
    right = left+10
    filter = (x >= left) & (x <= right)
    ax.plot(x[filter]-left,y[filter], c='g', label="Data" if section == 1 else '')
    ax.plot(x[filter]-left, f[filter], c='r', linestyle=":", label="Fit" if section == 1 else '')
    left = right
    section += 1

ax.set_xlabel("x (modulo 10)")
ax.legend()
#plt.savefig("fig/mod.png", dpi=300)
plt.show()