The Dottie number

import numpy  as np
x = 1
for i in range(1000):
    x = np.cos(x)
print(x)

import numpy as np
from matplotlib import rc
import matplotlib.pyplot as plt

# Use LaTeX throughout the figure for consistency
rc('font', **{'family': 'serif', 'serif': ['Computer Modern'], 'size': 16})
rc('text', usetex=True)
# Figure dpi
dpi = 72

def plot_cobweb(ax, f, x0, nmax=40, filename='cobweb.png', *args):
    """Make a cobweb plot.

    Illustrate the behaviour of iterating x = f(x) starting at x = x0.
    args are parameters to the function and ax is the Matplotlib Axes to plot
    the convergent cobweb on.

    """

    # Iterate x = f(x) for nmax steps, starting at (x0, f(x0)).
    px, py = np.empty((2,nmax+1,2))
    px[0], py[0] = x0, f(x0)
    for n in range(1, nmax, 2):
        px[n] = px[n-1]
        py[n] = f(px[n-1], *args)
        px[n+1] = py[n]
        py[n+1] = py[n]
        print(py[n][0])

    # Plot the path traced out by the iteration.
    ax.plot(px, py, c='tab:blue', lw=1)

    # Annotate and tidy the plot.
    ax.minorticks_on()
    ax.grid(which='minor', alpha=0.5)
    ax.grid(which='major', alpha=0.5)
    ax.set_aspect('equal')
    ax.set_xlabel('$x$')
    ax.set_ylabel(f.latex_label)
    return ax

class AnnotatedFunction:
    """A small class representing a mathematical function.

    This class is callable so it acts like a Python function, but it also
    defines a string giving its latex representation.

    """

    def __init__(self, func, latex_label):
        self.func = func
        self.latex_label = latex_label

    def __call__(self, *args, **kwargs):
        return self.func(*args, **kwargs)

func = AnnotatedFunction(lambda x: np.cos(x), r'$\cos x$')

# Plot the function y=f(x) and the line y = x.
x = np.linspace(0, 1.5, 500)
fig = plt.figure(figsize=(600/dpi, 450/dpi), dpi=dpi)
ax = fig.add_subplot(111)

# Plot y = f(x) and y = x
ax.plot(x, func(x), c='#444444', lw=2)
ax.plot(x, x, c='#444444', lw=2)
ax = plot_cobweb(ax, func, -1, 100)
# Customization to set appropriate plot limits.
ax.set_xlim(0, 1.5)
ax.set_ylim(0, 1.5)

plt.savefig('dottie.png', dpi=dpi)
plt.show()