## Tools to Explore Collatz Space

##### How to Download Python

This page will teach you how to download Python and how to install the various Python modules you'll need to run my programs. Don't worry! I'll walk you through step by step so it's easy.

##### #1 - Show a Single Collatz Hailstone

This program fires a single Collatz Hailstone. For your choice of input n, this program will calculate where that hailstone eventually ends up (loop_seed or div...), and tell you the stopping time and max value.

##### #2 - Input xa+b, Output the Two Graphs

This program takes in a choice of xa+b and outputs the

two classic graphs, stopping times and max value.

##### #3 - Expeditions through the Collatz A-B Plane

This program lets you send out a "space-probe" through

the Collatz a-b Plane, gathering info as it goes.

It can bring back the following kinds of data...

1. A print-out of the Loop_seeds in those worlds.

2. The same info presented as a Loop_Seed graph.

3. Info on things like All_Conv? or All_Div? or 1_Looped?

4. Videos of Paths Through the a-b Plane.

##### #4 - Studying the Divergent Entries

This program is designed to examine an entirely different

part of the Collatz World - the divergent hailstones.

These have never before been explored and mapped before now.

Will there be structure? Will there be total chaos? Let's find out!

##### #5 - Dissecting the Graphs, one

##### branch at a time

This program is designed to break down the traditional two graphs - stopping times & max values - one branch at a time, first asking you to choose one loop, then one branch, then the next branch, etc... exploring your way up the tree.

##### #6 - Branches and Their % Memberships

This program is designed to test for the % membership of individual branches in any desired Collatz space.

##### #7 - Ripping Apart the Tree Diagram

I am currently undertaking a quest to unlock the secrets of the Tree Diagram, in particular the pattern and structure underlying the science of when new orange branching nodes are created and which roles are they assigned? This program assist with that study.

##### #8 - Blue Name Sequences

This program lets you choose an orange branching node of x3+1 space and determine its Blue Name Sequence.

PS: I have countless other programs and have studied much beyond what is posted on this website in many directions. If you want more tools, feel free to contact me.