A Graphical Representation of the Collatz Problem

Inspiration

I have a passion for mathematics and have analyzed the Collatz Problem in the past. I am fascinated by the fact that it is so simple yet remains unsolved, and wanted to obtain a graphical representation of it to enhance my understanding.

What it does

The program produces a graph that plots positive integer values against the number of steps required for said integer values to converge to a 4, 2, 1 sequence. I have included programs with different maximum integers to show the scaling of the graph.

How I built it

I used python to develop my graphical rendering.

Challenges I ran into

I encountered many syntax errors and had to learn to use a variety of Python functions.

Accomplishments that I'm proud of

I am proud of the fact that I was able to produce this model on my own and create a visible product while learning about python and other programming languages.

What I learned

I learned about numerous functions in python, important python libraries, and information about other programming languages.

What's next for A Graphical Representation of the Collatz Problem

The Collatz Problem has significant implications for computer science, as well as a host of other scientific fields. To date, there has been no algorithm developed capable of predicting long-term trends in the Problem (as we have no information of the sort), and its non-computability could be used to define the boundaries of both computing and mathematics in executing commands and solving problems. Furthermore, according to J.H. Conway, "there is a generalized 3x+1 function whose iteration can simulate a universal computer." This cements the connection between the Collatz Problem and computer science, as any insight on the Problem could entail advancements in humanity's understanding of universal computers. While my graphical representation may not be able to directly provide insight on the Collatz Problem, an analysis of my code and its results could potentially lead to developments regarding the Collatz conjecture. A number of patterns can be detected using my graph, and these patterns could be incorporated into other algorithms in order to yield significant results.

Built With

• python