A python script that plots the cobweb diagrams of the iterative tent map. This script uses the python 'decimal' library to avoid floating point arithmetic error propagation. This plot will run until the iteration values "escapes" (i.e. reaches a value > 1)

tent_map_cobweb.py

from decimal import Decimal, getcontext
import matplotlib.pyplot as plt

# Set the desired precision
getcontext().prec = 28

# Define the tent map function using Decimal for high precision
def tent_map(x, r):
    half = Decimal('0.5')
    return r*x if x < half else r*(1-x)

# Generate the cobweb plot with Decimal and stop if value goes above 1
def cobweb_plot(x0, r, max_iterations):
    x0, r = Decimal(x0), Decimal(r)

    # Prepare the figure
    plt.figure(figsize=(10, 10))

    # Dense grid of x values for plotting the tent map and y = x line
    x_values = [Decimal(x)/Decimal('1000') for x in range(1001)]  # Decimal range 0 to 1
    y_values = [tent_map(x, r) for x in x_values]

    # Convert Decimal lists to floats for plotting
    x_values_float = [float(x) for x in x_values]
    y_values_float = [float(y) for y in y_values]

    # Plot the tent map and y = x line
    plt.plot(x_values_float, y_values_float, 'b', label='Tent Map')
    plt.plot(x_values_float, x_values_float, 'k--', label='y = x')

    # Cobweb diagram
    x, y = x0, Decimal('0')
    for _ in range(max_iterations):
        y = tent_map(x, r)
        # Draw vertical line
        plt.plot([float(x), float(x)], [float(x), float(y)], 'g', linewidth=2)
        # Draw horizontal line
        plt.plot([float(x), float(y)], [float(y), float(y)], 'g', linewidth=2)
        # Update the point
        x = y
        # Stop if the value goes above 1
        if y > 1:
            break

    plt.title(f'Cobweb Plot for r={r} starting at x0={x0}')
    plt.xlabel('x')
    plt.ylabel('Tent Map Value')
    plt.legend()
    plt.grid(True)
    plt.show()

# Initial point, scaling coefficient, and number of iterations
x0 = '0.05'
r = '3'
max_iterations = 20

# Generate the cobweb plot with Decimal
cobweb_plot(x0, r, max_iterations)