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18 vectors
Yesterday, while guarding the entrance for the retro game day, I looked at the problem of finding at the
35 vectors. I have been looking at finding
collections of eighteen vectors at the Haming distance of four from a vector.
The reason why there are eighteen is because there are only six ways to change
two of the four zeros into ones and at most three nonoverlapping pairs of ones
that are changed into zeroes. I realized that there are some restrictions as
to how for three patterns of zeros that are changed into ones that only
differ at two locations, such as for example, 1100, 1010, and 0110, the way
the ones are changed into zeros must all be different. Because if they are the
same, the Haming distance is only two. I got the idea that there were only four
configurations, not counting all kinds of symmetries. But when I was at home, I
wrote a program, which produced 19 solutions. Which meant that either I was
wrong or the program. Today, I wrote the following animation to display the 19
solutions. The three colours refer to the three ways in which zeros are changed
into ones and the three lines refer to the patterns in which the ones are
changed into zeros. Any of the 21 possible lines cannot have two colours and
there cannot be a point where to lines of the same colour meet.
In the evening, I realized how there eight combinations of three vectors, such
as in the example, and that these can be visualized as the triangles of the
octahedron. And also
that each edge represents the lines of two colours and that there are only
three possible patterns of these, namely, where the lines are a cycle of six
lines, a cycle of four lines and a path of two lines, or a path of six lines.
This put a lot of restrictions on how the various patterns can be placed on
the octohedron, and that that is a good way to determine all unique (with
respect to symmetries) combinations of 18 vectors there are.
Granduncle
Today, my mother became a greatgrandmother, because the oldest son of my
youngest sister became a father. It also means that I have become a granduncle.
Rainbow at Gogbot
While waiting with some other volunteers for the introduction tour along all
the locations of the Gogbot festival, we saw
a rather bright, double, and complete (as far as I could see) rainbow. I took several pictures, one of which is shown to the right. After the opening, at eight, I helped
out as a guard in the Grote Kerk because there were a lot of visitors. I stood
near the entrance, close to The Mictobial Vending Machine by Emma van de Leest, one of the few artist being present at the exhibition
in this location and explaining her project to visitors. Also close were the
Pink Chicken Project,
Al¿ve, and
Caravel. There was not
much interaction or moving projects as in some of the previous years and
several vistors commented about this to me while leaving the venue. At eleven,
after the exhibition closed, I went to the Metropool concert room to have a
peek at the Gogbot lift off // Experimental Electronics & Modular
Night, which was free for volunteers, only to discover that they had very
strict rules with respect to bags and coats, and that the small lockers
costed two Euro each. I was a little disappointed, because I had hoped to
work a little on my notebook while listening to the music, and decided to go
home.
Gogbot
I was a guard at the former VVVbuilding. The first half on the second floor
and the second half on the third floor. These floors had all the Young Blood
nominees, selected from the graduates of the various art academics in the
Netherlands. I found the following nominees mentionable (roughly in the order
I encountered them at the exhibition):
The building also had the projects by the freshman students of the Creative
Technology major of the University of Twente. I used the Embryo'matic
to 'create' a designer embryo from Stork Industries. Mine was #10293 and I had
to 'pay' $4929. In the evening, I again, helped out at the Oude Kerk, because
some volunteers wanted to have dinner and one did not show up (or left early).
1773 constellation
I continued working on the 18 vectors problem (which is related to the
KABK wrapping paper) and this evening, I worked
on a program to calculate the number of unique ways the octahedron can be
tilled with the 19 patterns I found on September 1. I
arrived at a program which calculates in how many ways the edges can be marked
with on of the three possible patterns, such that they are compatible with the
19 patterns. Such a 'constellation' does not neccessary match a solution of the
patterns and even if it does, there could more than one. The program found
1773 such constellations. When at home, I thought about a different approach
for finding the solutions for the 18 vectors problem.
Book
I recieved the book KiloGirls written by Julia Luteijn in English, which I bought
from the author for € 13.90 (including postages).
Tetem
I went to Tetem art space to look at
the exhibition Xenobodies in Mutation. At the ExploringLab some people were assembling a
small motor powered by solar cells. I also joined and assembled one.
54718 solutions
I continued working on the program to calculate
the number of different solutions of 18 constant weigh vectors 'around' a
vector with seven ones and four zeros, where around means at a Haming
distances of four and such that all vectors are at distance of at least four.
The program found 54718 different solutions taking in consideration all
possible permutations of the 'rows' of the vectors.
Book
At 17:43, I bought the book What Do Women Want?: Adventures in the Science
of Female Desire written by Daniel Bergner, in English, and published by
Canongate in 2013, ISBN:9781782112563, from charity shop Het Goed
for € 1.95.
This months interesting links
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 August 2019