[r-t] Monster extent of triples

Philip Earis pje24 at cantab.net
Mon Oct 6 08:12:37 UTC 2014

In this week's Ringing World (page 1027) there is a very interesting article 
showcasing an exciting new extent of pure triples.  The article (by "Francis 
N. Steyn", who is reputed to share a computer terminal with a prominent 
four-in-hand ringer from the Midlands) explains the creation of a new, 
seemingly structureless, one-part composition of triples.

The starting point for the new extent was Andrew Johnson's 10-part of 
bobs-only Stedman. This was run through an algorithm to repeatedly chop and 
rearrange it until a completely new extent emerged.

The algorithm took a random change in the base extent, and then swapped the 
next change for one of the other two possible changes (eg 3.1 could become 
3.5 or 3.7). The choice of which change to insert was heavily weighted to 
equalise the occurrence of 1s, 3s 5s and 7s throughout the composition. The 
algorithm then reversed all the changes between the original (randomly 
chosen) starting point and an occurrence of the newly-chosen change. This 
produces a sequence of 5040 changes with a discontinuity...multiple 
applications of the algorithm led to the discontinuity disappearing thereby 
producing a true and fiendish new extent.

The place-notation for "Frankie's" new extent is copied below. It would of 
course be a very significant (though I feel and hope achievable) challenge 
to ring this.  It feels like an appropriate challenge for the ringing "x 
prizes" I proposed a while back.

Anyway, I have some questions:

1) Each change (ie 1, 3, 5 and 7) appears 1260 times in the new 
composition.The frequency of occurrences of the 12 possible 2-change blocks 

1.3    454
1.5    363
1.7    443
3.1    429
3.5    449
3.7    382
5.1    374
5.3    451
5.7    435
7.1    456 (457 if comp rotated)
7.3    355
7.5    448

Please can somebody also produce a similar table showing the frequency of 
the 108 possible 4-change blocks, and also all possible 6-, 8- change blocks 

2) What is the longest string of notation that appears 4,5,6,7,8,9,10,11 and 
12 (or more) times?

3) Who can come up with interesting results by applying the algorithm to 
existing extents on 5 or 6 bells?

4) Is there ever a "memory effect", ie how (if at all) can the choice of 
starting extent influence the "monster" chopped up extent produced?

Place notation for the new monster triples extent:

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