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Book
At 12:09:18, I bought the book Liefde is business by Arnon Grunberg
from bookshop Broekhuis for € 4.95.
Between pages 102 and 103, I found a beer felts from Chiangmai German
Microbrewery & Restaurant. Possibly someone took this book to Thialand
on holiday.
Magnolia more dead than alive
About a month ago, we placed the small magnolia
tree in a bigger pot outside in the garden. Soon the leaves started to turn
brown, probably because it was much colder outside than inside, especially
because it has been rather cold in the past weeks, except for last week. Now
two new leaves have appeared and a third is on the way. Only one of the new
leaves is clearly visible in the
picture on the right, and it has been partly consumed by some kind of
insect (caterpillar). Although it looks more dead than alive, it looks like it
will survive after all.
'Volume' of icosahedron
In the past weeks, I thought about the
'volume' of the icosahedron. It has 12 vertices, 20 faces and 30 edges. For this we need
to observe all the possible vertix colourings with the colours A, B, C, and D.
Because all the faces are triangles, and have to be coloured with a different
colour taken from α, β, and γ, it follows that each edge
colour will be assigned to 10 edges. This means that the Kempe chains in the
dual graph (a docecahedron) of each type (αβ, βγ, and
αγ) will have a total length of 20. This could either be one chain
of two chains, because the chains must be a multiple of 4 and larger than 5,
only the combination of a chain with length 8 and a chain of length 12 is
possible in case of the two chains. If for each type of Kempe chain it would
be possible to have two chains, it would be possible to have 3.3.3 = 27
different points, meaning that each edge could theoretically be assigned a
different point, because 12 is smaller than 27. It could be possible if this
is the case for one of the types, because 3.2.2 = 12. However, if we try to
colour the edges when there is a chain of length 8, it turns out that this is
not possible. Furthermore, for each vertex colour there will be exactly 3
vertices with that colour. And all the vertices of the same colour will be
assigned the same coordinate. A rather boring result. There are four types
of faces with respect to the colours assigned to the vertices, and we can count
for each type how often the edge colours appear clock or counter-clock wise.
It seems that the 'volume' is equal to three tetrahedron between the four
points, when adding and substracting the facse by orientation.
Carina Schüring
This evening, Conny and I visited the workshop
of Carina Schüring somewhere outside of
Enschede. Despite some weather radar indicated that it might rain, we decided
to go there by bike. We did not encounter any rain during our trip and also saw
some sun. On the way back we made a small detour through the village Usselo.
Carina had beautifully arranged all her works of the past years on the wall of
her workshop as kind of private exhibition for us. She had made us tea and
served it with some biscuits. The window was open and you could hear the birds
chirping. For her, it was also a long time ago that she had seen all her works
together. We just enjoyed looking at her works in the calm atmosphere of her
workshop and talking about various subjects. A very special evening for all
three of use, as I understood. (On the top right a picture of a part of the
wall.)
She already had thought about how much she wanted to ask for the work that
impressed me so much during the 'AKI finals 2015'
exhibition. For her the price is not so much determined by the dimensions
of the work but the emotional value it has. The price was above what I
initially had in mind, but now that I have met her and know what value she
attached to it, I realize that it is a good price. I am seriously taking it
into consideration.
Havannah versus Hex
Havannah and Hex are both connection games, but slightly different because the first is a racing
game and the other is not. Lets restrict the connection games to those games
where players take turns in marking one position with their colour (in real
play this is often done by placing a stone with thier colour on a location on
the board) and where there is a collection of winning patterns that when marked
by the same colour result in a win for the player who first marks the locations
defined by the pattern. Futhermore, there are no restrictions on which
locations can be marked at any point in the game. This to exclude games like
Connect Four.
The connection games can be divided into games where the winning patterns are
the same both for both players or where they are complementary, in which case
they are often symmetric in the sense that on the basis of some transformation
rule there is a one-to-one mapping between the winning patterns for both
colours. Usually there is a simple rule that describes all the winning
patterns. (Because usually the first player has a significant advantage over
the second player, often the pie rule is introduced, which allows the second
player to switch colours after the first move, thus preventing the first player
to make a move that would asure victory.) For all connection games it is
theoretically possible to determine the optimal strategy leading either to a
win or to a draw.
A connection game does not belong to the category of racing games, when every
winning pattern for one of the players excludes all winning patterns for the
other player. If this is the case for a connection game where the winning
patterns are the same for both players, it means that all patterns must
include more than half of a number of key locations. For this reason these
kind of games must be kind of boring and will have a rather simple winning
strategy for the first player. For this reason non racing connection games,
usually will be like Hex, where the winning patterns are complementary.
Another important property of connection games is whether they are drawless.
This is the case when it is not possible to mark all locations with either
colour such that there is no winning pattern for either player. Hex is
drawless and for Havannah not, although the number of markings without winning
patterns is very small.
It is not the case that all non racing connection games are also drawless. One
could think of a variant of Hex where a simple straight connection between
two sides is not a winning pattern. Probably this variant is not very
interesting because it is relatively easy to prevent the other player from
winning. Games with a low number of draw positions are generally considered
more interesting. I do not know whether it must be the case that all connection
games with draws must also be racing games.
The winning patterns in racing games can often be divided into patterns that
are tactical and patterns that are strategic. Tactical winning patterns are
patterns that are easily prevented by the opposing player. They usually contain
a low number of locations (such as the small cycle patterns in Havannah) or a
limited set of key locations (such as the bridge patterns in Havannah). The
presence of tactical winning patterns adds flavour to racing connection games,
while they are probably not possible in non racing games.
I guess, I will start working on a formalisation of connection games, like I
did for Havannah.
(follow-up)
Book
At 13:10, I bought the book Omgaan met kunst en natuur: Jo en Marlies Eyck
in Wijlre with text by Henk van Os and photographs by Kim Zwarts
from thrift store Het Goed for
€ 1.00 (including a € 0.05 tip). It contains pictures
from to works by Peter Struycken. Op page
22 there is a picture of Komputerstrukturen 2 under the title Computerstructuur zwart wit
4-69. This is the only published picture of this work that I know of.
There is a picture from the Struycken Structuur<->Elementen
exhibition on which this work is also visible. On pages 41 and 42 there are
pictures of Piet 5 under the
title Piet v.
Institute for art history
Today, Peter Struycken and I visited the
Netherlands Institute for Art History, also
known as RKD in Dutch. On forehand, we had made some requests about the
materials we wanted to see, but soon it became clear that our small selection
was far too large to be studied in one day. We started to work on the notes
that Carel Blotkamp compiled for a catalogue of works, which, as it seems,
was used for the 1974 exhibition. For
this he send forms to all people owning works of Peter Struycken. Many of the
works were know to me, but we also found some works that I had never seen
before. Our greatest find was a panorama picture of P. Struycken - Structuur '67 exhibition on the back of which Peter had
written all the Roman numbers of the works. This might resolve some of the
riddles with respect to the Structuur '76 works. Peter also told me
about the research he is doing with respect to the use of colours starting
from the early Greeks in 500 BC.
Flowers in magnolia
I noticed some flowers in our magnolia. Many of
them are in new branches. Here a picture of one of the flowers.
Havannah versus Hex (part 2)
On July 18, I wrote about the complexity of Havannah versus
Hex and said I would be working on a formalization of connection games. I
made it a little broader, and wrote something on the formalization of abstract strategy games, which is actually a rewrite
of a formalization of Havannah that I wrote
some years ago. Yesterday, I found Havannah and TwixT are PSPACE-complete. It was already known that
Hex is
PSPACE-complete.
According to the
Wikipedia page about game complexity, Havannah (size 10) has a higher
complexity than Hex (size 11). The numbers for Hex are from the article
Games solved: Now and in the future by
H.Jaap van den Herik, Jos W.H.M. Uiterwijk, and Jack van Rijswijck, which quotes the master thesis
Computer Hex: Are bees better than fruitflies? by Jack van
Rijswijck as it source. But after a quick scan through the thesis, I did not
find those numbers. Possibly they are taken from one of the referenced
articles. That Havannah (size 10) has a higher complexity than Hex (size 11)
could be the result of the fact that the first more than double the positions.
Book
At 13:43, I bought the book Zwerver by Johan Kelder from
bookshop Broekhuis for € 2.50.
This months interesting links
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