Saturday, 15 August 2026

ODD + and EVEN - Improved Format

Some time ago I got Gemini to carry out an analysis for me of attractors and vortices in the range up to 40000 under the ODD + and EVEN - algorithm. I copied the output into a Google document that listed: 

  • each attractor and how many captives it had
  • each vortex (along with the vorticals that comprised it)
  • the number of captives the vortex had
Here is the information the 193 page document displays for the attractor 39642:
  • Attractor: 39642
  • Captive Count: 395
  • Captives: [38997, 39017, 39035, 39037, 39039, 39053, 39055, 39059, 39063, 39065, 39070, 39071, 39072, 39073, 39074, 39075, 39076, 39077, 39078, 39083] ... (and 375 more)
Here is the information the documents displays for the vortex [38013, 38012, 38006, 37995, 38028]:
  • Vortex (Vorticals): [38013, 38012, 38006, 37995, 38028]
  • Captive Count: 564
  • Captives: [37055, 37075, 37097, 37099, 37107, 37123, 37125, 37127, 37133, 37135, 37137, 37139, 37141, 37143, 37145, 37149, 37150, 37151, 37152, 37153] ... (and 544 more)
The attractors and vortices are arranged in descending order by number of captives. The information is readily accessible but I thought I'd use Gemini again to improve the formatting of the document to make it more readable. Figure 1 shows the opening page of the 137 page document and Figure 2 shows the second page.


Figure 1


Figure 2

The document lists the attractors in ascending order and also in descending order by number of captives (see Tables 1 and 2 for the start of each table).


Table 1


Table 2

The document goes on to list vortices in ascending order and also in descending order by number of captives (see Tables 3 and 4):


Table 3


Table 4

Overall the document provides an excellent organisation of the data and I'll roll this out this the results for the ODD - and EVEN + algorithm and the PRIME + NON-PRIME - algorithm in the near future.

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