collatz_conj.py

import matplotlib.pyplot as plt
%matplotlib inline


def collatz(x, b=False):
  if x % 2 == 0:
    if b:
        print(f'{x} is even, {x}/2 = {x/2}')
    return x / 2
  else:
    if b:
        print(f'{x} is odd, {x}*3 + 1 = {x*3 + 1}')
    return 3*x + 1

def compute_iterations(x, b=False):
  iter = 0
  y = x
  max = y
  while y != 1:
    y = collatz(y, b)
    if y > max: max = y
    iter += 1
  print(f'{x} required {iter} iterations')
  return (x, iter, max)


def graph_collatz():
    x_axis, y_axis, max_axis, m, m_x = get_data()
    plt.plot(x_axis, y_axis, 'b.')
    plt.plot(x_axis, [m for i in range(1, len(y_axis)+1)], 'r--')
    plt.plot([m_x for i in range(1, len(x_axis)+1)], y_axis, 'r--')
    plt.xlabel('Numbers')
    plt.ylabel('Number of iterations')

    
def graph_max_collatz():
    x_axis, y_axis, max_axis, m, m_x = get_data()
    plt.plot(x_axis, max_axis, 'r-')
    plt.xlabel('Numbers')
    plt.ylabel('Max number while getting to 1')
    
    
def get_data():
    collatz = [compute_iterations(i) for i in range(1, 100000)]

    x_axis = [a for (a, b, c) in collatz]
    y_axis = [b for (a, b, c) in collatz]
    max_axis = [c for (a, b, c) in collatz]

    m = max(y_axis)
    print(m)
    m_x = x_axis[y_axis.index(m)]
    print(m_x)
    print(max(max_axis))
    
    return x_axis, y_axis, max_axis, m, m_x

graph_max_collatz()