Collatz_conjecture

What's Collatz conjecture ?

The Collatz conjecture is defined as follows:

• The starting value n is a positive integer
• If the previous term x is even, the next term = x/2
• If the previous term x is odd, the next term = x*3 + 1

The conjecture is that whatever the value of n, the sequence will always reach 1 before oscillating indefinitely on the values 4,2,1,4,2,1,4,2,1, .... (in this program, the sequence generation process stops as soon as it encounters a 1). The Collatz conjecture is still an unsolved problem in mathematics, it has not yet been shown that all sequences reach 1 for an integer and positive initial value.

What does the program do?

The program designed with PyQt5 and PyQtGraph generate Collatz conjecture sequences. The program allows to:

• Visualize graphically a sequence from a single input value
• Compare the sequences of two input values in the form of two superimposed graphs
• Display more detailed statistics (flight time, time on altitude >n, max altitude, average altitude, number of even/odd values)
• Save graphics in .png format
• Copy the sequence(s) generated to the clipboard
• Randomly generate Collatz sequences

Screenshots

Interface

Sequences pasted from clipboard

Graph saved as .png image

Requirements

• numpy
• PyQt5
• pyqtgraph
• pyperclip