Number to Brocot

import matplotlib.pyplot as plt
import numpy as np

def find_fraction_for_number(target_number, steps):
    pL, qL = 0, 1
    pR, qR = 1, 0
    pM, qM = 1, 1  # Start with the fraction 1/1
    path = []
    for _ in range(steps):
        if pM / qM < target_number:
            path.append('R')
            pL, qL = pM, qM
        else:
            path.append('L')
            pR, qR = pM, qM
        pM, qM = pL + pR, qL + qR
    return path

def plot_path_for_number(path):
    positions = [0]  # Starting position
    current_position = 0
    for move in path:
        if move == 'R':
            current_position -= 1  # Move down for 'R'
        elif move == 'L':
            current_position += 1  # Move up for 'L'
        positions.append(current_position)

    plt.figure(figsize=(10, 6))
    plt.plot(positions, linestyle='-', marker='', color='blue')
    plt.title(f'Path to Approximate {target_number}')
    plt.xlabel('Step Number')
    plt.ylabel('Vertical Position (Down for R, Up for L)')
    plt.grid(True)
    plt.show()

# Example: Approximate the number e (2.718281828459045)
target_number =  2.7182818284
steps = 40  # Adjust the number of steps to refine the approximation
path = find_fraction_for_number(target_number, steps)

plot_path_for_number(path)