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At 13:23, I took a picture of the sundail on the Old Church at the city center, which at noon, can show the approximate date. Unfortunately, the sun was not so bright, so the shadow of the sundial is not really sharp.
In bookshop Broekhuis, I looked at the exhibition on the third floor, which was part of the month of the print. I did not see anything interesting. At 13:44, I purchased a black, hardback Moleskine Daily Diary / Planner of 2014 (ISBN:9788866135647) for € 16.95.
At Galerie Objektief, I met with Wil Westerweel, whoes pictures were on display. I gave me a free CD with many of his pictures. Hence, I went to Rijksmuseum Twenthe to see the exhibition Paths to Paradise because I discovered that it included four works by Peter Struycken. It took me some time to locate the four works, because the works were ordered by theme and works for very different ages and thus from very different styles, where combined. I found it a little odd to find the highly abstract works by Struycken between figurative works. I also looked at the "Please do not touch. Even clean hands can damage." installation by Annelies Doom. It consisted of the small shelfs attachted on the wall. The first had two white cloves to handle valuable objects, and the remained shelves had one book for evey word, where the thickness of the book seems to be related to the emphasis given to the word. The book for "not" was the thickest. From the fact that some of the soft covers had curled-up, it seems that the books had been touched. (Later, at home, I discovered that the nine books had an ISBN, namely: 9789461902405, and were published by Uitgever Digitalis. but it's not available.
I also looked at the exhibitions Bart Hess. A Hunt for High Tech, which I did not find interesting, and Renie Spoelstra. Het dode punt van de schommel, that I found intriguing after I understood the idea and process by which the works were made.
Finally, I went to Tetem art space, where I looked at Hybrid Skins and 100 jaar grafiek uit ene particuliere collectie (100 years of prints from a private collection).
all 00 12
3 3 1 1
4 6 2 3
5 9 2 6
6 22 8 13
7 40 10 29
8 100 33 66
9 225 57 167
10 582 168 413
11 1464 366 1097
12 3960 1061 2898
13 10585 2646 7938
14 29252 7514 21737
0 1 2 a b c d b a e f c g h i d j k l e l j k f h i g g c d b h f a e i k l j j d b c k i g h l e f a
Given a sequence of 0, 1, and 2, the above table can be used to calculate the value for the sequence, by starting with 'a' and calculate for each element in the string another value by using the above table. Now it appears that whenever you end with 'a', that the sequence is a sequence that can be generated from 00. For sequence generated from 12, you get one of 'b', 'i', or 'k'. I guess it will not be very difficult to prove this, by the effect of rules for replacing two digits by three digits in the generation step. Below the table extended with the number of sequences ending at the given letters:
all 00 12 'b' 'i' 'k'
2 2 0 1 0 1 0
3 3 1 1 0 0 1
4 6 2 3 1 1 1
5 9 2 6 2 3 1
6 22 8 13 4 6 3
7 40 10 29 12 8 9
8 100 33 66 19 23 24
9 225 57 167 60 56 51
10 582 168 413 146 135 132
11 1464 366 1097 370 361 366
12 3960 1061 2898 951 984 963
13 10585 2646 7938 2714 2611 2613
14 29252 7514 21737 7226 7255 7256
15 80819 20209 60609 20285 20189 20135
16 226530 57233 169296 56520 56426 56350
17 636321 159080 477240 159376 158879 158985
18 1800562 451928 1348633 449392 449753 449488
19 5107480 1276870 3830609 1278053 1276311 1276245
When studying the transition one can see that each column has all the letters from 'a' to 'l' exactly once, meaning that they are permutations of each other. It is well known fact that any set of permutations is related to a finite group. The table can be used to construct the following group (with 12 elements):
* 0 12 21 22 01 10 1 11 20 02 2
0 * 21 12 10 1 22 01 20 11 2 02
12 21 * 0 1 10 01 22 02 2 11 20
21 12 0 * 01 22 1 10 2 02 20 11
22 01 10 1 2 20 11 02 12 0 21 *
01 22 1 10 11 02 2 20 0 12 * 21
10 1 22 01 02 11 20 2 21 * 12 0
1 10 01 22 20 2 02 11 * 21 0 12
11 02 2 20 21 12 0 * 1 22 10 01
20 2 02 11 12 21 * 0 01 10 22 1
02 11 20 2 0 * 21 12 22 1 01 10
2 20 11 02 * 0 12 21 10 01 1 22
In this table '*' stands for the empty sequence, and it also happens to be the identiy element. This is the Alternating group A4, because it is the Von Dyck group with, for example, a is 12, b is 10, c is 02 and a2 = b3 = c3 = abc = e. (See also: Alternating group A4 (tetrahedron) Cayley graph and table.)
I made this drawing of graph representing the transition table I constructed over the weekend. The arrows with the red triangle are the transitions for 1, and with the blue triangle the transitions for 2. The light grey lines, connecting opposite points, represent the transitions for 0 in both directions. The green lines represent some transitions for 211 or 122 and the purple lines for 221 or 112.