main_live_graph_infinite.py

import matplotlib.pyplot as plt


#Graph setup

plt.xlabel('iteration')
plt.ylabel('value')
plt.title('Graph')


#Variables

number = 1 # initial positive number
iterations = 0 # to count iteration 
List_iteration= [0] # lists to plot
List_number= [0]



#Interaction
print('\n Do you want to start from a specific number [y/n] ?')
option_number=str(input(' default is 1, enter y or n to continue : '))

if (option_number == 'Y' or option_number == 'y'):
 
    number =int(input(' Enter the number : '))

print('\n Press Ctrl + C any time to quit \n')
start=str(input(' Press Enter to begin ! \n'))

num = number  


while True:
 
     if(num%2) == 0:  #if number is even make it odd
        num = int(num/2)
        iterations += 1 #increment

        List_number.append(num) # Add number/value in list, every time
        List_iteration.append(iterations) # Add iteration value/increment
        plt.plot(List_iteration, List_number , 'b-o') #Pass varibles as arguments to plot, with graph style
        plt.pause(0.0001) #pause for interval seconds
                           # graph figure, will be updated and displayed before the pause (show data ploting live/animation)


     else: 
         num = int(num*3+1)  #if number is odd make it even
         iterations += 1

         List_number.append(num) # Add number value in list, every time
         List_iteration.append(iterations) #iteration
         plt.plot(List_iteration, List_number , 'b-o') 
         plt.pause(0.0001)
 
     if(num == 1): #Next number !
        print(' Number : ',number, ', Iterations : ',iterations, ', True ', '\n' )
        number += 1 #increment
        iterations=0
        num = number

        List_iteration=[0] # reset/empty lists for next round
        List_number=[0]


     elif(num == 0): # conjecture break , alert !
         print(' Number : ', number, ', False ', '\n' )
         plt.show() # show ploted graph
         break #exit loop