[Python] Coding a bifurcation diagram

I was wondering what was wrong with my code as I keep getting a weird but similar result to the actual bifurcation diagram. I am using the iterative equation xn+1 = xn * r(1-xn).

Here is my code:

import numpy as np
import matplotlib.pyplot as plt
from functools import lru_cache

@lru_cache(maxsize = 1000)
def bifunc():
R_val = []
X_val = []
R = np.linspace(0.5,4,1000)
for r in R:
x = 0.5
for iterations in range(1001):
x = x*r*(1-x)
R_val.append(r)
X_val.append(x)

plt.plot(R_val, X_val, ls = '', marker = ',')
plt.show()

bifunc()


Here is the image that keeps coming up:

Any help would be appreciated. Thank you.

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