Question

PYTHON PROGRAM!

Exercise 1 - The Collatz Conjecture

The Collatz conjecture was a mathematical proposal set forward by Lothar Collatz in 1937, also known as the 3n + 1 conjecture.

The conjecture is summarized as follows:

1. Start with any positive integer
2. if that number is even, divide it by 2
3. otherwise (i.e. if it's odd), multiply the number by 3 and add one (hence 3n + 1)
4. repeat until (and if!) the resulting number is 1

For example, if you start with 12, the series would be 12, 6, 3, 10, 5, 16, 8, 4, 2, 1, and takes 9 iterations to get to 1.

The Collatz conjecture says that any starting number will eventually end up at 1. However, it is still unproven (see Mathematician Proves Huge Result on ‘Dangerous’ Problem (Links to an external site.) for some recent progress!).

Collatz visualization

Write a python program that will determine how many iterations it takes for each starting value from 1 to 100 (experiment with higher values if you want!). Write out the starting value and number of iterations to a comma delimited csv file (i.e. one set of comma separated values per line). Also plot the result (starting value vs. iterations) with a visible marker for the points (you can choose which ever style you like) and no line. Make sure to give your plot a title and label the axes appropriately.

Answer 1

Code: Logic to find number of iterations for starting value ranging from 1 to 100

• I have stored starting values in list l_val and number of iterations in list l_itr

​
l_val = []
l_itr = []

for i in range(1,101):
    val = i
    itr = 0
    
    while val != 1:
        itr += 1
        
        if val%2 == 0:
            val = val/2
        else:
            val = 3*val + 1
            
    l_val.append(i)
    l_itr.append(itr)
    
print("For starting value =", l_val[11], ", No. of iterations =", l_itr[11])

Code to save CSV file:

• Use zip() to write values in comma-seperated format

import csv

with open('sample.csv', 'w') as fp:
    writer = csv.writer(fp)
    writer.writerows(zip(l_val, l_itr))

Code to plot:

• I have used matplotlib package to plot the graph
• See the code to understand how to put a title and label the axes.

import matplotlib.pyplot as plt

plt.plot(l_val,l_itr,'-or')
plt.title('Collatz conjecture', fontsize=18)
plt.xlabel('Starting Value', fontsize=16)
plt.ylabel('Number of Iterations', fontsize=16)

Plot:

PS: Let me know if anyone face any issue or have some doubts.