It is possible, as shown here, to put an extra set of obtuse diagonal braids between those used in my 18x18 tour, to cover any size area, but they cannot be incorporated in a tour since they leave isolated cells uncovered at intervals of {0,3} moves, as if the whole board is composed of centreless 3x3 boards. All other cells are used.
This is a tour I constructed yesterday, partly inspired by some work by Robert Bosch on twitter, showing patterns on 24x24 boards. This is a closed tour on the 18x18 board which has 90 degree rotational symmetry (birotary symmetry as I call it). It features complete diagonal braids of oblique angle type. It is based on the familiar 6x6 tour of this type.
I have revised the page on "Simplified Spelling" on my website, and also the "Anthology of Well-Known Verse" which shows well known pieces in the new spelling scheme.
Here is a summary of the spelling scheme as it now is. Largely unchanged: a, b, d, e, f, g, h, i, k, l, m, n, o, p, r, s, t, u, v, w, y, z. Redefined: c = 'sh' sound in 'ship', 'match'; j = 'zh' sound in 'ridge' 'leisure'; q = 'th' in 'then'; x = 'th' in 'thin'. Ambiguities: u as in 'cut' or 'put'; Indefinite vowel sound shown as a or r. Longer vowel sounds consist of a, e, i, o, u followed by a, i, u or by r, y, w if vowel follows. These may be reduced to a single letter at the end of a word.
Some new spellings: 'church' becomes tyurtc, 'judge' becomes dyudj. The indefinite article 'a' stays as a or becomes ei according to pronunciation. Similarly the definite article 'the' becomes qa or qi. I have given up trying to distinguish between the u sounds in 'cut' and 'put', or using a special letter for the indefinite vowel sound. This means more current spellings are unchanged.
I just managed to get round to updating my profile on this Blogger account, so that it now shows my current location, Crewe instead of St Leonards on Sea. It took a lot of trial and error before I could locate the page to make the updates. It also had my old email address, long out of date. I've left the same photo of myself as I was back in 2009 when I started this Diary.
I decided to take a longish walk this morning,
since I haven't been getting much exercise.
These are some of the photos I took along the way
For unknown reasons these have not appeared in the sequence in which they were taken.
These are images that I put on twitter, partly stimulated by work by Robert Bosch.
They show ways of combining repetitions of a symmetric tour in an array 2x2, 3x3, 4x4 to form a single larger symmetric tour. The odd case simply uses a series of Vandermonde style links (two deletions and two insertions). The even cases use a linkage octagon (four deletions and four insertions) around the centre point, and the centre of each quarter in the 4x4 case.
The tours used are from Wenzelides 1849 and Haldeman 1864.
Some photos from 30 August and 3 September.
