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bool valid_UTF8(const unsigned char *s) { while (*s != 0) if ( *s < 0x80 || ((*s & 0xe0) == 0xc0 && (*s & 0x1e) != 0 || ((*s & 0xf0) == 0xe0 && ((*s & 0x0f) != 0 || (s[1] & 0x20) != 0) || (*s & 0xf8) == 0xf0 && ((*s & 0x07) != 0 || (s[1] & 0x30) != 0) && (*(++s) & 0xc0) == 0x80) && (*(++s) & 0xc0) == 0x80) && (*(++s) & 0xc0) == 0x80) s++; else return false; return true; }

AA AA AA AA AB AB AB AB AB AB AD AD AD AD AD AD AG AG AG BA BA BA BD CD DA DD AA AB BA BC CA DE AB BC BG CG DA DG AB BC DA AD CD EA BA BC BD BD BD BD BD BD BG BG BG CA CA CD CD CG DA DA DA DA DD DD ED EF AB AG BC CG EA EG AB BC EA FA FD FA FG FA AB BC BD CD BG CG DE DE DE DE DE DE DG DG EA EA EA EA EA EA ED ED ED EF EF EF EF EF AA AB BA BC CA GH AB BC AB AD BC CD HA HD AG CG HA AA AB BA CA HI EG EG EG FA FA FA FA FA FA FD FD FD FG FG FG GH GH GH GH GH HA HA AB BC HA AB AD BC BD IA ID AG BG IA AB BC IA AA AB BA BC CA AB AD HA HA HD HD HD HD HI HI HI HI IA IA IA IA ID ID ID ID BC CD AB AG BC CG AA AB BA CA AB AD BC BD AB AG BC BG

The impossible (partial) diagonal sequences are:

AABAG AABBD AABBG AABDG AABEA AABEG AABFG AABHA AABHD BABAG BABBD BABBG BABDG BABEA BABEG BABFG BABHA BABHD CABAG CABBD CABBG CABDG CABEA CABEG CABFG CABHA CABHD CADAA CADAD CADAG CBDAA CBDAD CBDAG BDDAA BDDAD BDDAG CDDAA CDDAD CDDAG AEDAA AEDAD AEDAG CEDAA CEDAD CEDAG AFDAA AFDAD AFDAG BFDAA BFDAD BFDAG CHDAA CHDAD CHDAG AABIDAA AABIDAD AABIDAG BABIDAA BABIDAD BABIDAG CABIDAA CABIDAD CABIDAG

However, when calculating the number of (complete) diagonal sequences, it shows that some diagonal sequences have no continuation, in the sense that there is no two longer sequence that is based on it. The smallest such example is the sequence "DAAHIFAAB". Note that this sequence is one of the impossible (partial) diagonal sequences mentioned May 20. There is only one way the top left part can be filled, namely with a three by three in the top corner and two one by two tiles with the longest side touching the left and top sides. When placed in a rectangle, this sequences has 62 different solutions in the right bottom part. However for the next (partial) diagonal sequence there are only eight different ways it is filled for these 62 solutions. When these sequences are extended with an 'A' on both sides, always the first three and/or the last three have no tile available, thus making them impossible for a (complete) diagonal sequence. Longer sequences that start or end with the "DAAHIFAAB" if (and maybe: and only if) they are followed or preceded with the sequence "DEB", which forces an 'A' for the next diagonal.

Below the updated table for the number of sequences per diagonal length.

l #dia #pat 1 2 3 4 5 6 7 8 ------------------------------------------------------------- 3 3 3 3 5 6 6 6 7 14 14 14 9 47 47 47 11 140 141 139 1 13 544 658 442 90 12 15 2616 3708 1868 446 260 42 17 15111 25750 8838 3392 1930 539 306 94 8 4

The latest version of the program also calculates the number of unique (with respect to rotations and mirroring) tilings inside rectangles of various sizes. The algorithm first calculates possible combinations of two rows for a given width, and next uses a recursive algorithm to find the number of patterns for a given height. This could be improved with a matrix transfer method and it is also possible to derive recurrence equations for each row (and column) for this table. Although the table is symmetric along the main diagonal, the numbers above and under the diagonal have been calculated independently to verify the correctness of the algorithm. (The output of the program also contains a table with all tilings.)

| 1 2 3 4 5 6 7 8 9 10 ----+------------------------------------------------------------ 1 | 1 1 0 0 0 0 0 0 0 0 2 | 1 1 1 0 0 0 0 0 0 0 3 | 0 1 2 0 1 2 1 4 5 3 4 | 0 0 0 0 1 1 1 0 2 3 5 | 0 0 1 1 2 4 6 12 28 57 6 | 0 0 2 1 4 0 18 33 49 105 7 | 0 0 1 1 6 18 8 77 195 687 8 | 0 0 4 0 12 33 77 166 1204 5135 9 | 0 0 5 2 28 49 195 1204 3217 29733 10 | 0 0 3 3 57 105 687 5135 29733 83306

Below the 166 unique street tiling patterns that fit in an eight by eight square.

Around 1 in the afternoon, I arrived at the Rijksmuseum where I met with Meindert. I first wanted to go to Room 3.4. Before getting there we saw three paintings by Karel Appel and a video of Imponderabilia by Marina Abramović and Ulay. In Room 3.4, I first went to look at the works:

*Dish Relief*by Jan Schoonhoven, 1963.*Relief with Segment*by Ad Dekkers (1938-1974), 1967.*Variation on Circles IV*by Ad Dekkers (1938-1974), 1965 - 1967.

*Splash*by Peter Struycken, 1974

*Bare Bottom Dress*by Marlies Dekkers, in or after 1993- Without title (known as 'postkantoorreliëf') by Jan Schoonhoven, 1958.
- Design sketches for Centraal Beheer building in Apeldoorn by Herman Hertzberger.

*The Crucifixion*by Jacob Cornelisz van Oostsanen, about 1507-1510. (In Room 0.1)- Memorial Tablet for the Lords of Montfoort, about 1400. (In Room 0.4)
*Landscape with an Episode from the Conquest of America*by Jan Jansz Mostaert, about 1535. (In Room 0.4)*The calling of St John during the marriage at Cana*by Jan Cornelisz Vermeyen, about 1530 - 1532. (In Room 0.6)*The Deposition and the Entombment*by 1290. Note 'carpenter' removing a nail from the feet of Christ. (In Room 0.2)*Portrait of a Girl Dressed in Blue*by Johannes Cornelisz. Verspronck, 1641. (In Eregalerij)*Gallant Conversation, Known as ‘The Paternal Admonition'*by Gerard ter Borch (II), about 1654. (In Room 2.25)*Still Life with Asparagus*by Adriaen Coorte, 1697. (In Room 2.24)*Jeremiah Lamenting the Destruction of Jerusalem*by Rembrandt Harmensz. van Rijn, 1630. (In Room 2.8)*Self-portrait*by Vincent van Gogh, 1887. (In Room 1.18)*La Corniche near Monaco*by Claude Monet, 1884. (In Room 1.18)*Portrait of Albert Verwey*by Jan Veth, 1885. (In Room 1.18)*The Singel Bridge at the Paleisstraat in Amsterdam*by George Hendrik Breitner, 1896. (In Room 1.18)*The Voorstraat Harbour in Dordrecht*by Willem Witsen, 1898. (In Room 1.18)*View of the Oosterpark, Amsterdam, in the Snow*by George Hendrik Breitner, 1892. (In Room 1.18)*Wooded View near Barbizon*by Johan Hendrik Weissenbruch, 1900. (In Room 1.18)

- Bo Lamers. A large self-portret is reproduced on the outside of the building. She also had a collage of painting and drawing, which I found less interesting.
- Annejet Riedijk. She had two videos and five paintings on display. I find her painting style very interesting. In a sense it is very vague and with odd colours, but yet it looks very realistic, almost like you watching reality through a kind of filter.
- Marcel Berwanger. He had a sketch book with experimental calligraphy that looked very interesting.
- Ilse Löbker. I found her
*Vertaalconcept*(*Translation concept*) rather interesting. - Joyce Rothman. Her combination of
linocuts and poems under the title
*Vluchten*(*fleeing*) was interesting. - Rahel Kausemann. I liked her design of her master thesis.
- Dieuwke Eggink. I especially found his three paintings of the same scene with different colours interesting.
- Huub van Stijn with his
*Atlas of Desolation*consisting of large sized book, a small booklet and a wall painting.

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

If we look at where the jellyfish each time the three swim movements have been performed, it turns out that there are eleven different sequences, which when marked with the letter 'a' to 'k', results in the following table:

a a a a a a a a a a b a c b a c a a a a a a d a a a c c b c c b a a a a d d d a c a a e e c a a a a a a a a a a e a c a a c a c a a a a a a f a e f e e e a a a a a a a f a f f a a a a e a c a a f f a f f a f f a a a a a a a a a a f a f f a a f a a a a a a a f g a a a a a a a a a a a a a g a g a a a a a a a a a a a a a a a g a a a a a a a a a h i i h a a a a a a a a a a h h i h h i a a a a a a h a a h a j h h h a a a a a a a a a h a k j h j h h a a a a a a h a k a k j h h h h a a a a a a a a h a k h a h h a

There are six sequences ('b', 'd', 'g', 'i', 'j', and 'k') with a length of 12 swim movements (where the letter of each sequence appears four times in the table), a sequence ('e') of length 24, a sequence ('c') of length 36, a sequence ('f') of length 48, and a sequence ('a') of length 516. The least common multiplier of the lengths is 6192. Actually, this is the least common multiplier of 516, 72, and 48. The real big question is if there exists a combination of three swimming patterns with an even larger repeat length. It seems that the jellyfish never make a complete turn from one swimming pattern to the next. (I have not verified this with the program.) It seems a good requirement to imposse on combinations of swimming patterns. Of course, one could also ask this question for smaller sized squares (or rectangles) and with different number of swimming patterns.

- 9: Listen to Darwintunes: random music evolving its way to beauty
- 9: Herringbone Wang Tiles
- 13: Three Gears are Possible - Numberphile
- 13: Sketches by GrgrDvrt
- 14: SYNTHI-JS is an emulator of the legendary EMS Synthi A modular synthesizer, built in JavaScript.
- 17: inconvergent
- 21: Organic core-sheath nanowire artificial synapses with femtojoule energy consumption

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