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I write, therefore I am

With this variation on a famous statement by the philosopher Descartes, I would like to express that the act of writing about what happens in my life is important to me.

Monday, May 23, 2016

Book

At 11:12, I bought the book Boezem by Edna van Duyn, Marinus Boezem, and Fransjozef Witteveen written in Dutch and English published by Art Books International Limited in 1999, ISBN:9789068682229, from charity shop Het Goed for € 6.50.


Saturday, May 21, 2016

The Things Network node

The past month, I have become a regular visitor of TkkrLab, a local hackerspace. Today, there was an opportunity to build The Things Network node consisting of a RN2483 Low-Power Wide-Area Network chop and a Chinese Arduino Nano clone. One of the organizers soldering the RN2483 chip to the PCB for me. I did the soldering for connecting the Arduino Nano to the PCB. One of the organizers also helped me testing the unit and it seemed to work using the TTNMapper Andriod App. I did not have a laptop available, so I could not create a user account for myself. In the evening, at home, I got the node to work after having some trouble with getting ttnctl to run (got an x509 error on Windows XP), connecting to the Chinese Arduino Nano clone (required driver for CH340 serial USB chip), and getting Arduino IDE to compile ttnmapperarduino (had to move library files to the proper location). It also looks like the signal is only picked up by the gateway in the center of the city when I put the node outside in the backgarden. I saw four 'ping' messages come through as a proof that everything works. Now I have to find some interesting application for it, and also find out how I can process the messages using MQTT.


Friday, May 20, 2016

Street Tiling: Diagonal - Corrected

Continuing from my research on Street Tiling Patterns, I discovered that previous presented results are incorrect. I changed the program to calculate the number of diagonal sequences starting from the sequences with length three. To my surprise, I stopped very soon. While debugging, I noticed that there was a tile with two B's on the right, while there is non with two B's on the left, meaning that the elimination algorithm for removing tiles that can never occur, was incorrect. When I corrected the error, two more tiles were removed resulting in the set:

 AA AA AB AB AB AB AD AD AD BA BA BA BA BC BD BD BD CA CA CD CD DA
 BD DA AA BA BC DE AB DA DG AD CD EA ED EF AB EA EG FA FD FA FG AB

 DA DE DE DE DE DE DG EA EA EA EA EA ED EF EF EF EF EF EG EG FA FA
 BD AA AB BA BC GH AB AB AD CD HA HD HA AA AB BA CA HI AB HA AB AD

 FA FA FA FD FG FG GH GH GH GH HA HA HA HD HI HI HI HI IA IA IA ID
 BD IA ID IA AB IA AA AB BA BC AB AD CD AB AA AB BA CA AB AD BD AB

But this did not effect the algorithm for finding all possible diagonal sequences. Next, I noticed that one sequence of length five being marked as impossible, was actually possible. This uncovered a huge bug in the algorithm for calculating impossible sequences. Now it no longer found impossible sequences with length five and the algorithm enumerating possible diagonal sequences returned many results. But I did find some diagonal sequences for which there was no next diagonal sequence. I changed the algorithm for finding impossible sequences such that it would not stop with length five. I made it search up to sequences of length 23. It found nine impossible sequences that all contain the subsequence "AHIFA". There are possible diagonal sequences that contain the subsequence "AHIFA". It is not possible to claim that these are all the impossible sequences, but there is reason to believe that this is the case. The sequences are:

   DAAHIFAAB
   DAAHIFADEBA
   DAAHIFADEBD
 ADEBAHIFAAB
 BDEBAHIFAAB
 ADEBAHIFADEBA
 ADEBAHIFADEBD
 BDEBAHIFADEBA
 BDEBAHIFADEBD
On could capture all these sequences with the regular expression ([AB]DEB|DA)AHIFA(AB|DEB[AD]). Below a table given results with respect to the number of diagonal sequences. The first column gives the length of the sequences, the second column the number of diagonal sequences, and the third column the number of patterns that exist till and including this diagonal. The rest columns explain the relationship between the number of sequences and number of columns. For the columns with the number n in the header, the number in the row tells how many sequences are related to n patterns with the sequences. The numbers in the row add up to the number of sequences, while the numbers multiplied with the number in the header of the columns add up to the number of patterns.

 l   #dia   #pat     1     2     3     4     5    6    7    8    9
------------------------------------------------------------------
 3      3      3     3
 5      6      6     6
 7     12     12    12
 9     30     30    30
11     68     69    67     1
13    178    210   150    24     4
15    483    636   354   105    24
17   1706   2684  1010   478   182     8    28
19   7452  13160  3582  2480  1086   160   144
21  35764  74566 13102 12242  7166  1320  1666   64  162   24   18


Wednesday, May 18, 2016

Book

At 11:18, I bought the book Eindexamencatalogus 2007 / ArteZ Academie voor beeldende kunsten Arnhem written in Dutch published by ArteZ Academie voor beeldende kunsten Arnhem in 2007, ISBN:9789086900916, from charity shop Het Goed for € 2.50.


Sunday, May 15, 2016

Art

I visited Rijksmuseum Twenthe. First I looked at the exhibition De Nieuwe Smaak (The New Taste). I liked the following works:

Next I saw the Thomas Gainsborough exhibition. I was not very impressed. The work I liked most is The daughters of the artist from around 1758.

From 12:01 to 12:17, I walked around The Rhythm Painter by Jaap Drupsteen. (impressions on vimeo.) After I looked around the rest of the museum, I came back and walked around from 12:38 to be another twenty or so minutes. In the rest of the museum, I liked:

  • Totem, women, birds by Karel Appel, 1951.
  • Structuur II A by Peter Struycken, 1967.
  • Structuur by Peter Struycken, 1967.
  • Structuur XXXXV by Peter Struycken, 1967. (I noticed that the colours change slightly.)
  • Falaises près de Pourville from 1882 by Claude Monet
  • Gezicht op de de Muurhuizen bij de Dieventoren te Amersfoort by Jan Weissenbruch, 1864

At 13:07:20, I bought the book De Nieuwe Smaak. De kunst van het verzamelen in de 21ste eeuw edited by Josien Beltman written in Dutch published by Rijksmuseum Twenthe in 2016, ISBN:9789072250421, from the museum for € 2.00.

Next, while on my way to TETEM art space, I decided to visit Kunstenlandschap (Art and landscape). At Tetem, I saw the following works I liked:

  • Sporen in het land by Ina Wolters
  • All grown up by Patricia van de Camp
  • 25 by Jans Muskee

The GPS-track of how I biked and walked in KML file for Google Earth or in Google Maps. Along the route I liked some works by: Nanon Muskee, Henk Slomp, Mark van Loon, and Imke Beek.


Saturday, May 14, 2016

Street Tiling: Diagonal

In the past week, I continued working on the program for Steet Tiling patterns with Wang tiles that I started developing on May first. This program first of all reduces the set of Wang tiles to those that can occur in combination with other tiles. This results in the following set:

 AA AA AA AB AB AB AB AB AD AD AD BA BA BA BA BC BD BD BD CA CA CD
 BD DA DD AA AB BA BC DE AB DA DG AD CD EA ED EF AB EA EG FA FD FA

 CD DA DA DE DE DE DE DE DG EA EA EA EA EA ED EF EF EF EF EF EG EG
 FG AB BD AA AB BA BC GH AB AB AD CD HA HD HA AA AB BA CA HI AB HA

 FA FA FA FA FA FD FG FG GH GH GH GH HA HA HA HD HI HI HI HI IA IA
 AB AD BD IA ID IA AB IA AA AB BA BC AB AD CD AB AA AB BA CA AB AD

 IA ID
 BD AB

Next, I wanted to know if it would be possible to construct an algorith that would fill one quadrant of the plane with a 'random' pattern, by completing a diagonal at the time. It would be nice to know that if one has finished a diagonal, it is always possible to fill the next, without having to back-track to the current. We look at filling the fourth quadrant. We define a diagonal sequences of colours that can occur on a path that alternating goes up and right, starting with an up movement from the first colour to the second and ending with a right movement between the last two colours. This means that the sequences are always of odd length. I wanted to find out which sequences are not possible. For the sequences of length three this is rather simple to derive from the above Wang tiles. For example the sequence III is not possible because there is no Wang tile in the above set that has I in the left bottom, left top, and right top corner. The program found the following sequences of length five and seven that are also not possible (excluding sequences that contain a shorter sequences that is already not possible. There are no sequences of length nine that are not possible (presuming that they do not contain impossible sequences of length three, five, and seven. This gives some hope that it is indeed possible to implement a back-tracking algorithm that fills the quandrant diagonal by diagonal, not having to back-track to a previous diagonal if the impossible sequences are avoided when filling a diagonal. The sequences are:

 BAABA BAABD BAAEA BAAEF BAAEG BAAFA BAAFG BAAHA BAAHD BAAHI BAAIA
 BAAID DAABA DAABD DAAEA DAAEF DAAEG DAAFA DAAFG DAAHA DAAHD DAAHI
 DAAIA DAAID ABABA ABABD ABAEA ABAEF ABAEG ABAFA ABAFG ABAHA ABAHD
 ABAHI ABAIA ABAID CBABA CBABD CBAEA CBAEF CBAEG CBAFA CBAFG CBAHA
 CBAHD CBAHI CBAIA CBAID EBABA EBABD EBAEA EBAEF EBAEG EBAFA EBAFG
 EBAHA EBAHD EBAHI EBAIA EBAID EBCBA EBCEA EBCEF EBCHA EBCHI FCAFA
 FCAFG FCAIA FCAID ADAAB ADAAD ADADA ADADE ADADG BDAAB BDAAD BDADA
 BDADE BDADG ADGDE AEAAB AEAAD AEADA AEADE AEADG CEAAB CEAAD CEADA
 CEADE CEADG HEAAB HEAAD HEADA HEADE HEADG AEGDE HEGDE AFAAB AFAAD
 AFADA AFADE AFADG BFAAB BFAAD BFADA BFADE BFADG IFAAB IFAAD IFADA
 IFADE IFADG AFGDE IFGDE AHAAB AHAAD AHADA AHADE AHADG AHAGH CHAAB
 CHAAD CHADA CHADE CHADG CHAGH AIAAB AIAAD AIADA AIADE AIADG AIAGH
 BIAAB BIAAD BIADA BIADE BIADG BIAGH

 AABABAA AABABAB AABABDA AABABDE AABABEF AABABGH AABDEBA AABDEBC
 AABDEBD AABEFCA AABEFCD AABGHEA AABGHED AABGHEF AABGHEG AABHIFA
 AABHIFD AABHIFG BABABAA BABABAB BABABDA BABABDE BABABEF BABABGH
 BABDEBA BABDEBC BABDEBD BABEFCA BABEFCD BABGHEA BABGHED BABGHEF
 BABGHEG BABHIFA BABHIFD BABHIFG DABABAA DABABAB DABABDA DABABDE
 DABABEF DABABGH DABDEBA DABDEBC DABDEBD DABEFCA DABEFCD DABGHEA
 DABGHED DABGHEF DABGHEG DABHIFA DABHIFD DABHIFG AADABAA AADABAB
 AADABDA AADABDE AADABFA AADABGH AADABIA AADADAA AADADAB AADADAD
 DADABAA DADABAB DADABDA DADABDE DADABFA DADABGH DADABIA DADADAA
 DADADAB DADADAD ABDABAA ABDABAB ABDABDA ABDABDE ABDABFA ABDABGH
 ABDABIA ABDADAA ABDADAB ABDADAD EBDABAA EBDABAB EBDABDA EBDABDE
 EBDABFA EBDABGH EBDABIA EBDADAA EBDADAB EBDADAD FCDABAA FCDABAB
 FCDABDA FCDABDE FCDABFA FCDABGH FCDABIA FCDADAA FCDADAB FCDADAD
 ADEBDAA ADEBDAB ADEBDAD BDEBDAA BDEBDAB BDEBDAD GDEBDAA GDEBDAB
 GDEBDAD HEDABAA HEDABAB HEDABDA HEDABDE HEDABFA HEDABGH HEDABIA
 HEDADAA HEDADAB HEDADAD AEFCDAA AEFCDAB AEFCDAD BEFCDAA BEFCDAB
 BEFCDAD CEFCDAA CEFCDAB CEFCDAD HEFCDAA HEFCDAB HEFCDAD IFDABAA
 IFDABAB IFDABDA IFDABDE IFDABGH IFDADAA IFDADAB IFDADAD AGHEDAA
 AGHEDAB AGHEDAD AGHEFCA AGHEFCD BGHEDAA BGHEDAB BGHEDAD BGHEFCA
 BGHEFCD AHDABAA AHDABAB AHDABDA AHDABDE AHDABEF AHDABGH AHIFDAA
 AHIFDAB AHIFDAD BHIFDAA BHIFDAB BHIFDAD CHIFDAA CHIFDAB CHIFDAD
 AIDABAA AIDABAB AIDABDA AIDABDE AIDABEF AIDABGH

These results are incorrect! read follow-up story.


Friday, May 13, 2016

Books

At 11:47, I bought the following two books from charity shop Het Goed:
  • ontplooid edited by Arno Kramer written in Dutch published by AKI in January 2001 for € 3.50.
  • AKI, Academie voor Beeldende Kunst en Vormgeving, Enschede: vijftig jaar kunstonderwijs by Erik Beenker, Dries Ringenier, and Geert Voskamp written in Dutch published by Uitgeverij 010 in 2002, ISBN:9789064504501, for € 4.50.


Wednesday, May 11, 2016

Link


Tuesday, May 10, 2016

Versaille pattern

I got interested in Street Tilings when I saw the Versaille tile pattern. This is pattern that repeats every six unit squares in both directions (without shift). I used my program to calculate all possible patterns and it found 78 of which only five have the same ratio of tiles as the Versaille pattern (including the pattern itself, of course). The patterns are displayed below. The title specifies the number of tiles of each size from small to large. For the Versaille tile pattern this is "4,2,4,2,0". The patterns are sorted by title.
This text is displayed if your browser does not support HTML5 Canvas.


Monday, May 9, 2016

Link


Sunday, May 8, 2016

Link


Friday, May 6, 2016

Temperature swing

Less than two weeks ago, the temperatures were very low for the time of the year. On April 26 the temperature reached below zero degrees Celsius and was at most nine degrees. On that day and two day before we even had some wet snow. Yesterday and today we had totally cloudless days and today the temperatures went up to 24 degrees. It seems that our small magnolia tree is not doing well as it seems that the new leaves has been damanged by the frost in the past weeks.


Sunday, May 1, 2016

Street Tiling - Wang Tiles

In the past week, I made some improvements with respect to the program that I wrote to generate Steet Tiling patterns. The latest version of the program can find all solutions up to an area of thirty in less than a day. I tried to add some more checks in the recursive back-tracking function, but it seemed that I hit some wall and that many simply made it slower. With each additional test to avoid parts of the search tree that are not going to find results, you also add some time to the execution of the function, adding a constant time to the total execution time. If a certain test is only effective in a rather small number of cases, this can lead to an increase in the total execution time. I thought about the idea to use Want tiles for the most restrictive case. I tried several coding methods. I came up with the idea to use the letters A to I to mark the unit squares of the tiles in the following manner:

   A  AB

   A  AB  ABC
   D  DE  DEF

      AB  ABC
      DE  DEF
      GH  GHI

If you look at all the ways these can be layed on a square grid, than the following 86 patterns can occur on the squares made up of two by two unit squares:

  AA AA AA AA AB AB AB AB AB AB AD AD AD AG AG BA BA BA BA BC BC BC
  BD CD DA DD AA AB BA BC CA DE AB DA DG AB DA AD CD EA ED AA AB BA

  BC BC BD BD BD BG BG CA CA CD CD CG DA DA DA DA DA DD DE DE DE DE
  CA EF AB EA EG AB EA FA FD FA FG FA AB BD CD GA GD GA AA AB BA BC

  DE DE DG DG EA EA EA EA EA ED EF EF EF EF EF EG EG FA FA FA FA FA
  CA GH AB GA AB AD CD HA HD HA AA AB BA CA HI AB HA AB AD BD IA ID

  FD FG FG GH GH GH GH GH HA HA HA HD HI HI HI HI IA IA IA ID
  IA AB IA AA AB BA BC CA AB AD CD AB AA AB BA CA AB AD BD AB

These are not exactly Wang tiles, because Wang tiles are labled on their edges, not their corners. But there are 28 different combinations of letters that occur on the edges, thus we could create an equivalent of 86 Wang tiles with 28 different 'colours' for the edges. This is a rather large number, and I thus thought about a way to create Wang tiles with less 'colours'. If one makes Wang tiles around the points where four unit squares meet, and use letters to indicate properties about the edges, I came up with the following set of 76 Wang tiles using nine 'colours' (0 and the letters 'a' to 'h'), where the order in which the 'colours' are give are top, left, right, and bottom side. Note that for every wxyz there is also a xwzy.

  0000 0ada 0ae0 0bda 0bf0 0cda 0cg0 0dga 0dh0 0ega 0fga 0fj0 a00e
  a0ad ab0b ac0b ad0b af0b b00f b0ad bab0 bb0c bbc0 bc0c bd0c bdb0
  bec0 bf0c bgb0 bhc0 c0ad cdb0 cec0 cgb0 chc0 d0ag dab0 db0b dbc0
  dc0b dd0b ddb0 dec0 df0b dg0b dh0b e0ag eb0c ec0c ed0c ef0c eg0c
  eh0c f0ag fdb0 fec0 fgb0 fhc0 gab0 gbc0 gd0b gdb0 gec0 gf0b gg0b
  gh0b hab0 hbc0 hd0c hdb0 hec0 hf0c hg0c hgb0 hh0c hhc0

I did search for algorithms or programs for analyzing Wang tiles, but I failed to find any. Last week, I came across a copy of the book Shadows of the Mind in which there is some reference to tiling the plane with copies from a set of polyominos.


Thursday, April 28, 2016

Link


Sunday, April 24, 2016

Hail and wet snow

Around eight in the morning, we had was a clear blue sky, which made me doubt the weather report that we would get hail and (wet) snow. But around 10:50 there was hail. The sky cleared again. But then again noon there was hail and also wet snow. And two hours later, again hail, that even covered the ground for some time. The temperature has been rather low for this time of the year. It is about 25 years ago, we had such low temperatures at the end of April. Last night the temperature drop to -0.7° Celsius. The highest temperature during the day, was just below seven degrees Celsius. The temperature graph below, clearly shows the drops in the temperature during the day that matched the periods of hail and wet snow. I read that some soccer was aborted due to snow on the field around here.

Insert only map

Often when I write a program, I make use of a simple single linked list to represent a mapping from keys to values. Sometimes, I even do not bother about the list being sorted or stored in the order the elements were added. Of course, there are containers available for this in the Standard Template Library and Boost, but these require me to import the whole library. This afternoon, I decided to implement a simple insert-only template for a program that I am working on. The template class InsertOnlyMap only has one method to find or insert a key to the map. The method will return a pointer to the value for this key, which might already have been present in the map or otherwise is added to it. Furhtermore, it defines an iterator that can be used to iterate over the values in the map. They key class should have a compare method, which return a integer representing the compare result. A negative value will indicate that the value is smaller than the one it is compared with and a positive value indicates that it is larger. The implementation is based on a binary tree that is being balanced on every insertion.


Saturday, April 23, 2016

Links


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Wednesday, April 20, 2016

Hexagons

An observation related to the Four colour theorem. Given two triangulations of a regular n-polygon. When these are placed inside a regular 2n-polygon such that vertices of this polygon alternatingly match with the vertices of the two n-polygons, then there can be found exactly n-2 'empty' hexagons in the pattern of lines of the triangulations of the polygons, where each hexagon consists of segments altenately taken from the two triangulations. The proof for this is rather simple. There must be a sequence of five vertices on the 2n-polygon, such that v1, v3 and v5 hava a triangle in one of the triangulations. There will also be a triangle attachted to vertices v2 and v4. The third vertice, vi of this triangle must be somewhere outside of the sequence. This is the only triangle that 'crosses' the first triangle, and also the other way around. The two 'crossing' triangles have a (irregular) hexagon with alternating segments from the two triangles. Now it is possible to construct two (n-1)-polygon with triangluations by removing the two triangles. Removing the first triangle is trivial because it is on the outside. To remove the second triangle, the edges v2 to vi and v4 to vi have to be merged. The various combinations for n equals six are shown on the top right using the colours red and blue for the two triangulations. The four hexagons are coloured white.

Link


Saturday, April 16, 2016

Street tiling patterns

I calculated the number of Street tiling patterns for various restriction with latest version of the program to see if maybe some of the sequences are included in The On-Line Encyclopedia of Integer Sequences®. I did not discover any of them, which either means that they contain errors or that nobody ever looked at them. The sequences are given below, were each column gives the number of unique street tiling patterns with respect to rotation and mirroring with stated area. The first row gives all the sequences without restriction. This also contains sequences that repeat themselves, thus have the same appearance as a sequence with an area that is a fraction of the area. These are excluded in the second sequence. This sequence still do contain points where four tiles meet (indicated with 'x') and that contain H-shapes (indicated with 'H'), and where some of the vertices in the H-shape might actually have four edges instead of the three that the H-shape might suggest. The following sequences have additional restrictions on the occurences of the number of tiles that meet in a point and the occurence of H-shapes. The 's' signifies the additional restriction on the size of the tiles, restricting them to one by one, one by two, two by two, two by three, and three by three.

area 1,2,3, 4, 5, 6, 7,  8,  9,  10,  11,  12,  13,   14,   15
--------------------------------------------------------------
all  1,4,6,24,25,98,93,386,520,1453,1749,8817,8398,30110,63789

xH   1,2,4,15,22,75,90,330,499,1375,1745,8507,8393,29825,63684
 H   0,1,1, 5, 6,17,21, 59, 73, 172, 208, 633, 649, 1620, 2479
x    1,1,2, 5, 9,13,25, 39, 67, 114, 188, 401, 567, 1088, 1932
     0,0,0, 1, 2, 3, 6,  9, 13,  24,  31,  59,  68,  126,  165

xH s 1,2,2, 9, 9,39,28,137,139, 447, 343,2163,1286, 5769, 8533
x  s 1,1,1, 3, 4, 4, 8,  9, 17,  21,  28,  61,  63,  109,  156
 H s 0,1,0, 2, 1, 4, 2,  9,  5,  14,   8,  40,  18,   49,   43
   s 0,0,0, 1, 1, 0, 2,  1,  1,   2,   3,   6,   5,    5,    6


Friday, April 15, 2016

Link


Thursday, April 14, 2016

Links


Monday, April 11, 2016

Introduction

Diaries
May 2016
April 2016
March 2016
February 2016
January 2016
2016
2015
2014
Alzheimer's Disease
Trip to China 2010
-- contact --

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My life as a hacker
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Puzzles

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cutting sticks
Califlower fractal
more...


Katla

Earthquakes
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