\begin{equation} x_{n+1} = r(x_n)(1-x_n) \end{equation}
In [ ]:
%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)