[r-t] Fw: Avon Double Cyclic Doubles

[Philip Earis]

John Bissell has sent this reply to my recent email, which I am forwarding 
with his permission.  Please see his questions below...

-----Original Message----- 
From: J. J. Bissell
Sent: Friday, July 24, 2015 3:38 PM
To: pje24 at cantab.net
Subject: Re: [r-t] Avon Double Cyclic Doubles

Dear Philip,

Yes that’s correct. Someone mentioned to me that the extent of Banana 
Doubles has a call every 12 rows, and that made me wonder whether it’s 
related (derived from?) a 24 rows per lead principle. So I generated the 
extent, and translated it to give it both cyclic lead heads and the double 
half-lead symmetry property. Of course, the translation makes it wrong 
hunting on the front (a method we’ve nicknamed Nova), so I finished with a 
rotation.

This prompts a further question: is it always possible to translate a plain 
course extent principle to give it cyclic lead heads? If so, why?

For example, noting that Avon Doubles has a parity change every row, I 
thought it would be interesting to see if there exists a plain course extent 
principle with half-lead double symmetry such that the row parity changes 
every six rows. This is what I came up with:

Parity Doubles: 3.1.3.5.3.125.3.5.3.1.3.145.3.5.3.1.3.145.3.1.3.5.3.125

Now, if instead one adopts

1.3.5.3.125.3.5.3.1.3.145.3.5.3.1.3.145.3.1.3.5.3.125.3

(i.e., starts from the second row), then one recovers the cyclic lead heads, 
half-leads, and quarter leads; though personally I prefer the right-hunting 
on the front rotation:

Parity Doubles v2: 3.125.3.5.3.1.3.145.3.1.3.5.3.145.3.1.3.5.3.125.3.5.3.1

I’m sure there must be a very simple reason for this, but it is not obvious 
to me.

Thanks,


John