I have been thinking about boundaries of subsitution patterns for irregular grids of squares and equilateral triangle. If there are two
irregular grids that are the same except for some changes in a closed area such
that there is a single boundary where on the inside the grids are different
while on the outside is the same, then this boundary has certain properties.
The corners on the inside of this boundary cannot be smaller than 150°,
because otherwise it is not possible to fill it in more than one way and is it
thus not possible that it is on the inside of an area that can be filled in
more than one way. For a corner with an angle of 150° one of the sides is
touched by a triangle and the other by a square. For a corner with an angle
of 180° in one alternative both sides have are touched by a triangle
while in the other they are touched by a square. For a corner with an angle
of 210° the same holds as with an angle of 150°. For corners with
angles of 240° and 300° it is possible that in the alternatives the
sides are touched by the same shape or by different shapes. Corners with an
angle of 330° is not possible, because the corner on the outside is too
small to fit anything. There are some more restrictions on angles of
consecutive corners due to the shapes on the outside. I think it is possible to
write a program that generates all possible boundaries, with increasing area,
and see if they can be filled with at least two different patterns, such that
the shapes on the inside are different. This could start with assigning
different assignments of triangles and squares on the inside of the boundary
and see if with this assignment the area on the inside can be filled.
I read some post on
Hacker News about Algol 68 Genie. That reminded me that in my first year at the university
we had to write programs in Algol 68. I also (vaguely) remember some story that the compiler that had
some bug that caused it malfunction on some programs during a few months of the
year and that instructors told students to wait a month and try again. This was
probably not the Algol 68 compiler developed by the Dutch branch of
Corporation and released in 1974. According to A Shorter History of Algol68 in which it says: "Zoethout ea, CDC Netherlands 1974.
Full implementation, used mainly in teaching in Germany and the Netherlands on
CDC mainframes". The report describing the compiler is: Algol 68, Version I, Reference Manual. The document describing the
development of this compiler An early implementation of revised algol 68 makes mentions of the
CDC 6000 series.
According to the document Informatica aan de THT, fase 01, 1974 - 1981, this compiler was used at
the university (then still called 'Technische Hogeschool Twente'), but I
remember that we worked on a DEC 10 mainframe that was installed in 1975.
The report A
History of Algol 68 mentions Algol 68C, a portable compiler that also made available for the DEC-20
mainframes. Also A brief history of Algol 68 Genie makes mentions of the Algol 68C compiler
on the DECsystems 10. I have a book by Cornelis H.A. Koster, Th.A. Zoethout, and H. Meijer, Systematisch
programmeren in Algol 68, published in 1978, about systematic programming
in Algol 68.
I came across the interesting blog Things they didn't teach you about Software Engineering, which I think
described the reality of software engineering quite well.
In the past years, I discovered that my greatest struggle with software
engineering is my deep rooted sense of insecurity. Software engineering is a
rather demanding task. I think it is one of the more creative types of
engineering, where the product of the engineering is not the design for a
system, but where the product is the system itself in the form of code.
Furthermore, there are usually many different solutions for a problem and many
different ways to express those solutions in code. With software engineering
there are often also many single points of failure. You have to live with the
reality of bugs that can express themselves in the most unexpected ways.
Professional software engineering is usually done in teams where you have to
work together with others on a single code base and where it is common that
your colleagues review you code or at least come across it when they have to
implement some feature or fix a bug. I often find myself worrying a lot
whether the solution I have chosen is the right one or whether I have tested it
enough. It is a common experience that you think you have tested all cases just
to discover that you missed some. Either you learn to hide your insecurities or
they drive you on a road to soul searching, possibly resulting in various forms
of burn-outs, in alienation from your family and friends outside of you work
circle, in changing your world view and/or in losing your faith. But which might in the end result in a
form of enlightenment.
At Concordia, I saw the exhibitionKunst en
Koffie with art works (mainly prints) from their art lending collection.
There was also a price list for items that you could buy. Some of the works
that I found most interesting, drawings or paintings from houses on a water
front, where not in the price list.
I wrote the program irst_sub.cpp to
find substitution patterns for irregular grids of
squares and equilateral triangles. The program implements the ideas I
expressed last week, which generates all boundaries that
can be filled with at least two alternating patters. I wrote some code to
visualize the solutions. While studying, I found another alternative coupling.
It looks similar like one of the two I found before. It is shown below:
At 17:36:49, I bought the book Historische atlas NL: Hoe Nederland zichzelf
bijeen heeft geraapt written by Martin Berendse and Paul Brood in Dutch
and published by Wbooks on Monday, September 2, 2019,
ISBN:9789462583177, from bookshop Broekhuis
for € 20.00.
This afternoon, Conny and I went to see the movieAvatar: The Way of Water. It is an impressive movie and a good sequal with
an open end to further sequals. Good balance between action and drama. Also
some interesting additions to the flora and fauna of Pandora, especially, the
introduction of the Tulkun, a sentinent race of whale like animals.
This afternoon, I visited the exhibitionUnderneath the wings of a butterfly at TETEM art space. I only saw the augmented reality part of the exhibition where you had to walk around the
room with a tablet to which headphone were attached. You had to follow a
butterfly. Interesting concept. There were a lot of flat photographs in the
scenery. I did not wait for the virtual reality part of the exhibition.
When we went walking this afternoon, there were some speck of snow falling from the sky, non of which stayed on the ground. On Friday,
there was some substantial snow in the Southern parts of the country but
nothing in our part of the country.
In the past weeks, I continued working on the program for find substitution
patterns for irregular grids of squares and
equilateral triangles. Below it shows 53 of the 15407 patterns with a
boundary length of 27 that the program found, starting with the pattern with
the smallest area. As can be seen, many of these patterns can be split in more
than one smaller pattern. I have wondered whether I should exclude these
combinations in the counts, but it should be noted that there are restriction
on how substiturion patterns can touch each other. The program does check if
the outside of the boundary can be filled with squares and triangles. It does
this by checking if the coves can be filled. The count of substitution
patterns per length of the boundary, starting with a length of 12, is: 1, 0, 1,
1, 4, 3, 12, 15, 44, 75, 200, 411, 1070, 2420, 6304, 15407, 40569, 104145. I
have not found this sequence in The On-Line
Encyclopedia of Integer Sequences®. The counts are given below.
Conny and I went to Museum No Hero where we saw two exhibitions. First we saw the exibition Oog in Oog met de Wereld
(Eye to Eye with the World). The works that I found noteworthy (all of
them, if I am not mistaken):
Citronella-lemoncouloured Tokyo Beauty Privacy Love, Elke Krystufek, 2000.
Lena, Cornelia Schlieme.
Braut, Wermer Liebmann, 2020.
Nabb nut nacktem Oberkörper, Stephen Balkenhof, 1996.
From the exhibition Verzamelen is kleur bekenen. De wilde collectie van
Geert Steinmeijer (Collecting is showing your true colours. The wild
collection of Geert Steinmeijer), I found the following works noteworthy.
In the past weeks, I spend some time working on my page about Dune 2021 film where I compare the transcript with the book, a script
and the screenplay. For this I watched most of the film and attempted to
count the number of shots in every scene. It
was interesting to watch it in such a detailed way, because it made me aware
of the sometimes subtle symbolism of certain shots. The most obvious being the
various shots of the ox. Another example is the shot of Paul closing his fist
with the ducal ring inside followed by a shot of the open hand of Leto hanging
This months interesting links