A new version of the Collatz Calculator is about to be released to the Apple App Store. The changes are somewhat experimental since they do not behave in a manner I would prefer but I wanted to get the functionality out for others to play with. If you are not familiar with the original version it is documented here. It is also important to be familiar with a design principal of the caclulator, that it will work across any Mx+B linear equation with both (M, B) pairs that work much the same way as 3n +1, that is (M, B) pairing that is what I call a member of the Colldilocks Set. This provides a means to study the effects of changing the (M, B) values and determine the behavior of individual sequences so that you can see which starting numbers will ultimately reach the value 1, and in the cases where the (M,B) pair is not a member of the Colldilocks Set, which numbers will result in an infinite loop or an infinite expansion.When using a non-Colldilocks pair, the graphml file will show the loopbacks, but knows when to stop when it encoulters an infinite expansion (Hint: No resolvable sequence will ever exceed n^3 *M. This way you can easily see which pairs produce a fully connected directed graph for the Colldilock pairs, and the broken sequences for the non-Colldilock pairs.

The latest version of the calculator introduces a memory as well as the capability of producing a graphml compliant file that can be used to graph the Collatz sequences. The memory is simply the collation of generated sequences. It is much more complicated to use at present, since all it does is take the current memory, generate the graphml description, and copy the result to the paste buffer. So to take advantage of this you would have to open your favorite text editor (Pages?), start a new document, paste the contents of the paste buffer into this new file, and export it as a plain text file and save it to the filesystem. At this point you would have to change the .txt extention to a .graphml extension. Once this is done, you can load it into any graphml viewing software such as the desktop application yEd from YWorks or even use their yEdLive website. I probably should mention that I receive no compensation from YWorks, that I don’t know and have not communicated with any of their employees, but am a long time user of their free version of yEd. So just to make sure I am clear, I have received no compensation of any type from YWorks, and they have received no money from me. But I love their application and am a very satisfied non-paying customer.

I probably should apologize for the Ta-Da effects. Even though you were able to disable this yourself through the app settings, I have decided that apps should be told to do things, but not heard unless something really really really needs to be communicated.

Let me know if this sounds intriguing, and feel free to send comments and or requests. I should mention that I also have the intent to release a windows version that will do arbitrary precision integers so that you can use virtually unlimited length integers, but constrained by the limits of the computer. Hey, even 32GB RAM is finite. Interested?