Sorry math students, I have described every Cantor set (within the limitations of MAX_SAFE_INTEGER of course)!
Please visit https://bambery.github.io/cantor_3-4_react/ to play with nowhere-dense sets.
Using the UI, select the number of segments to divide the interval into. Next, select the segments you wish to have removed with each iteration. Third, select how many iterations you wish to view, keeping in mind that the more iterations, the less comprehensible the graphics will be. Additionally, the denominator must stay below 253 - 1: due to this, I have restricted the number of iterations to maximum of 10. I could not justify a switch to BigInt, but please feel free to message me with reasons why it might be interesting.
After pressing "Cantor-ify!", you will see a graphic representing the intervals for each Cantorian iteration with a table listing the endpoints. All tables can be downloaded into a csv with the "Download This Data" button at the top.
This is a react rewrite of a small proof of concept that I hacked together: https://github.com/bambery/cantor_3-4 to demonstrate asymmetrical Cantor sets. I described this set originally by accident when I misinterpreted a midterm question while studying under Dr. Wilfredo O. Urbina-Romero at Roosevelt University in 2022.
I attempted to find a software license that would allow for general, non-commercial use and modification with accreditation, but this appears to not exist. I only allocated one story point to this task: therefore at this time, there is no license to use this software or any contents presented herein. If you wish to use or modify this codebase, please feel free to contact me and I will provide permission. You may reproduce this work without modification with accreditation back to me without permission.
When I have suitable time to allocate time to investigate, I will find and attach a suitable license. You can check where that is ranked on the Trello for remaining tasks.
This repository will, once a license is determined and attached, be provided free to those who wish to play around with Cantor-like sets with flexible constraints. The code is written to avoid recursion and be generally comprehensible to those with basic coding and mathmatical skills, and can be extended to cover additional scenarios if desired. No promises made on the quality of the React code, as this was my first React app 😄.