top of page

Chapter 5.6: The Relationship Between the Stopping Time Graph and the Tree Diagram

             So if we think all the way back to the beginning of this research project, my original obsession was with these three pictures, the three classical ways to visually represent the x3+1 world:

Screen Shot 2020-04-18 at 10.22.22

             While I've mostly been spending my nights and days thinking about the two images on the left (especially the Stopping Times Graph), other mathematicians have taken an entirely different approach to the problem and have gotten lost out in the maze of the Tree Diagram to the right. I never really thought my research would contact theirs... until something absolutely wild happened!

I had the following epiphany one night...

Take the standard x3+1 stopping times image:

Screen Shot 2020-04-18 at 10.22.15

        Logarithm the x-axis and zoom in on the bottom:

Screen Shot 2020-04-18 at 10.51.23

         You get this image:

Screen Shot 2020-04-18 at 10.53.48

         If we draw all the connecting arrows, we get:

Screen Shot 2020-04-18 at 10.54.48

         And now we perform the following wild transformation!...

Revealing that the Stopping Times Graph actually was the Tree Diagram in disguise all along!

Can you see it now?

Screen Shot 2020-04-23 at 7.06.29 PM.png
Screen Shot 2020-04-23 at 7.06.37 PM.png

This cool discovery has played a key role in almost all of my research that has followed thereafter. 

Screen Shot 2020-04-18 at 10.22.15
Screen Shot 2020-04-18 at 10.25.57
bottom of page