python code for for mathematics graph

Question

wrote some Python code to plot the coordinates of simple one dimensional linear mapping using matplotlib

Can someone tell me what's wrong with my code?

import matplotlib.pyplot as plt
import numpy as np

result = [10]
result[0] = 1
a = 1.1
x = np.linspace(0, 10, 10)

for i in range(len(result)):
    result[i+1] = a*(result[i] - 1/2) + 1/2
    plt.plot(x, result[i], 'ro')

plt.xlim(0, 10)

plt.ylim(0, 10)

plt.axhline(0, color='b', ls='-', lw=0.5)

plt.axvline(0, color='b', ls='-', lw=0.5)

plt.xlabel(r'$x$', fontsize=18)

plt.ylabel(r'$x_{n+1}$', fontsize=18)

plt.title(r'Graphs of $x_{n+1} = a(x_{n}-\frac{1}{2}) + \frac{1}{2}$', fontsize=20)

plt.show()

error message

 Traceback (most recent call last):
    y[i+1] = a*(y[i] - 1/2) + 1/2
    IndexError: list assignment index out of range

Answer 1

suppose the length of result is $n$, then $i$ in the for loop can attain value $n-1$, then you are accessing the $(n-1)+1=n$-th element of result.

However, in Python, the index starts from $0$ and the last index is $n-1$ but you are trying to acess the $n$-th element, hence that is why you have index out of range.