\begin{equation}
x_{n+1} = r(x_n)(1-x_n)
\end{equation}


```python
%matplotlib inline
# see https://youtu.be/ovJcsL7vyrk?t=322 for more context

# The following program carries out the iterative calculation stated above,
# sweeping across different values of r.
# n == number of iterations (x-axis)
from logistics_bifurcation import *
for r in reversed_logspace(2.9,3.84,num=200):
    fig, ax = plt.subplots()
    scat = ax.scatter(np.arange(NUM_ITER), get_series(r), marker="+")
    ax.set_title(f"{r=}")
    ax.set_xlabel("number of iterations")
    if np.isclose(r, 3.83, atol=1E-2):
        ax.set_title(rf"{r=},$\approx$ period 3!")
    plt.show(block=False)
    plt.close(fig)
```

58b4a212a46ef827c85d87474199ed473aacfce2
ipynb
Jupyter Notebook
bifurcation.ipynb
OceanNuclear/Chaos
926c627b35a8ef921af5f32b22845ca58b102f7d
MIT
bifurcation.ipynb
OceanNuclear/Chaos
926c627b35a8ef921af5f32b22845ca58b102f7d
MIT
bifurcation.ipynb
OceanNuclear/Chaos
926c627b35a8ef921af5f32b22845ca58b102f7d
MIT
Qwen/Qwen-72B
1. YES
2. YES