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3D piano fractal
Through a tweet by Cliff Pickover, I was directed to website Robert Fathauer: art inspired by mathematics and nature where I found
Three-Fold
Development, which reminded me about the
Fractal Jigsaw that I worked on last year. I thought about remaking this
with a 3D printer. Then I noticed the remark that it was based on a 3D model
by Henry Segerman. He has written the
interesting book Visualizing Mathematics
with 3D Printing. A
collection of designs can be found on Thingiverse. I did not find the
design for the Three-Fold Development. I spend some time figuring out the
design myself, making some drawings. I also have been thinking about the
different transition methods. I also got the idee to use a 3d printer to make
the fractal jigsaw puzzles.
PH-BFR
I biked to Enschede Airport Twente to see the arrival of PH-BFR, a Boeing 747-400M, on its last flight, Flight KLM747, in order to
be taken apart here in Enschede. The plane landed at 13:05. It is the biggest
plane that ever landed at the airport. I found a
small map of the last part of the flight, which I guess, is about the part
we could see from the airport (except some part when it was behind trees). I
took fifteen pictures. Here on the right the one of the touch-down.
Book
At 17:31:48, I bought the book Observatoria written by Michiel Schwarz
in Dutch and published by Westland/Utrecht Hypotheekbank NV Amsterdam in 1980
from thrift store Het Goed for
€ 0.20.
Gigatron
In the evening, I went by car to Hack42, a hacker space in Arnhem to attend
a lecture about the
Gigatron TTL Color Computer.
About half way, it started to snow. First a little
bit, but it quickly is became stronger and the snow stayed on the road. The
traffic had to slow down at some points to below 50 Kmph. I did arrive in
time. On the way home, it has stopped snowing and the snow had started to melt,
but on the first part on the highway, it seems that the snow had frozen to
the road, because the wheels made a lot of noise, not allowing to drive faster
than 70 Kmph. At the second half it was possible to drive at a normal speed,
but I found most people driving at about 80 Kmph.
The Gigatron is a processor build with 36 TTL chips, an EPROM chip and a
32Kb ram chip. The design was made to include as less as possible chips. This
resulted in a 8-bit RISC processor design, which runs at 6.25Mhrz. They
managed to make it produce a VGA signal with 64 colours. They also programmed
an interpreter for a 16-bits language which processes the program when it is
not generating the VGA signal. They showed how it could be used to play the
breakout
game in colour. Thus improving on the design of
Steve Wozniak, with
the number of chips needed and the functionality. It should be noted that at
that time 32Kb ram chips where not available yet. They plan on making it into
a kit with a nice case around it. I am considering to buy one.
Amsterdam
I left at 8:16 from Enschede, hoping to arrive at 10:30 in Amsterdam. But half
way between Apeldoorn and Amersfoort the train stopped in the middle of
nowhere. It was announced that the overhead line had broken ahead of us, and
that the train had to return to Apeldoorn. We were adviced to go back to
Deventer and travel further over Zwolle. There were some more delays and it
was only at 12:52 that I arrived in Amsterdam. It was snowing, but the snow did not stay.
While on the train, I finished reading the book
The Seducer's Diary by Søren Kierkegaard, which I started reading on November 18 and
bought on December 14, 2013. I found the story to
be completely unbelievable, including its form.
In Amsterdam I went to bookshop Scheltema,
where at 14:37, I bought the following two books:
Next, I went to gallery andriessen
& Eyck to see the exhibition
Drawing & and
more showing drawing by five artist and a work that is not a drawing.
Peter Struycken was one of the artists. Besides
two drawings, there was also a large wall carpter. Although this day of the
exhibition there was no formal opening, but some of the artist, including
Peter Struycken and some of their relatives, came to visit. I also met
Antonietta Peeters and talked with her about her work.
Snow and rain
In the afternoon it snowed. At the end of the
afternoon, it started to rain. While biking around the city I encountered
three instances where cars (and one city bus) had hid each other. In all cases,
the damage seems minimal. I also one time encountered a car slipping. In the
evening, most of the snow on the roads had disappeared.
Hail, snow and rain
Around four in the afternoon, it started to hail. The hail was quite fine, but
still hurted when touching the skin. After about twenty minutes the hail
changed into snow. About an hour later it changed to
rain. In the west of the country there were a lot of traffic jams and problems
with trains. In the middle of the country 44 cm of snow was measured at one
location.
Street tile grammar
This weekend, I continued my research on the grammar for the horizontal
continuation for an infinite street tile
pattern. The program I had been working on, crashed due to heap exhaustion.
I already had discovered that I could reproduce the result of November 12 with the smaller number of states, if I would work go up,
instead by going down, which actually comes down to using the upside-down
encoding, like:
A AB
D DE DEF
A AB ABC
GH GHI
DE DEF
AB ABC
But it did not bring me much further. As a next step, I decided to develop
a version that does not store illegale
chains, after I verified that it did not matter. This program was able to find
all illegale sequences of lengths smaller than sixteen. I worked on developing
a grammar to encompass all sequences. This resulted in the following
regular
expression (spread over multiple lines for readability):
[ABC]A(ABC)*AA
|([ABC]AAD|[HI]D)(A?ABA?D)*(AAA|G)
|(([ABC]AAD|[HI]D)(ABD)?AA|[HI]AB)DDEFD(ABG|AA(DAB)?(DAAA|DG))
|(([ABC]AAD|[HI]D)AABC|[HI]AB)(AADEAA|AABA)(ABG|ABCA(DAAA|DG))
|[HI]ABG
|[DEFHI]A[DG]
I searched the internet for an online converter to DFA. I found Regex
=> NFA => DFA by CyberZHG. It uses a slightly different notation, so
I rewrote the above expression into:
(A|B|C)A(ABC)*AA|((A|B|C)AAD|(H|I)D)((A|ϵ)AB(A|ϵ)D)*(AAA|G)|(((A|B|C)AAD|(H|I)D)(ABD|ϵ)AA|(G|H|I)AB)DDEFD(ABG|AA(DAB|ϵ)(DAAA|DG))|(((A|B|C)AAD|(H|I)D)AABC|(H|I)AB)(AADEAA|AABA)(ABG|ABCA(DAAA|DG))|(H|I)ABG|(D|E|F|H|I)A(D|G).
It returend a nice graph, but it seemed not to be the most compact representation.
Below some of the long sequences of the different parts of the grammar are
given together with the lines that can be inferred from them:
89 states
I took a new approach to the Street Tile
Patterns and wrote another program.
The idea was to implement an alternative method to calculate the 'states'
of the DFA underlying the grammar. After I implemented it, I tried different
depth, discovering it found more and more states. But then I realized, that
many states might be equivalent. I found a method to determine equivalent
states, and discovered that depth six, no more states were found, thus
concluding that there are 89 states. I spend some time analysing the states
with an idea to put them into a diagram. This evening, I spend analyzing some
of the generated sequences on which I based the grammars, and discovered that
all those sequences make use of a rather limited subset of states. I need some
more time to construct a diagram.
Book
At 11:03:13, I bought the book Je bent wat je
doet written by Roos Vonk in Dutch and published by Maven Publishing in
April 2014, ISBN:9789491845017, from bookshop Broekhuis
for € 11.50.
I spend some more time working on the the Street
Tile Patterns. I established that each state can be reached from each
state. If this would not be the case, it would have some implications for the
infinite non-repeating Street Tile Patterns. I wrote a small program to see
if the states could be used to generate a random pattern (within a square)
without using back-tracking, and it turned out that it was not possible. I
guess there must be a method to connect the DFA with itself to determine how
to generate from a given sequence (matching the DFA) a sequence below it that
also matches the DFA.
WinterGo: First day
I played my first game of Go in almost a year. I played
quite agressive, to my own surprise. I made several invasions and almost killed
a black group in one of the corners. But in the end the black player found a
good move, to which I did not know the answer, tipping the scales in his
favour, forcing me to resign. On the right of the status of the board, just
before he made his last move to kill a lot of white stones.
In the past weeks, I continued working on the
Street Tile Pattern in an attempt to generate 'large' random patterns.
This evening, I succeeded in doing so with the
latest version of the program, but I am not very satisfied with the
patterns being generated, because they have a certain bias.
WinterGo: Second day
In the morning, I played against Francien. I played slower than
last year, but I still missed some important
moves and lost too many stones because I did not watch out enough. I played
black and lost with 16.5 points. On the right the state of the board at the
end of the game. White had captured 24 black stones and black had captured 13
white stones.
In the afternoon, I attended a game exposition of
Game 27
- AlphaGo Master vs Fan Tingyu. I did not fall asleep, which I guess means
it was a good exposition, because usually I do fall asleep during go workshops.
At nine in the evening, Erwin
Bonsma gave a workshop on how to solve the Rubik's cube from scratch by using a trick to find your own
algorithms. I used it to derive some algorithms for my own method for solving
the cube. I have method that uses a minimum of algorithms, some very simple
ones that I would not even call algorithms anymore. The methods starts with
solving the edge pieces, and uses one algorithm (and it mirror) to move all
edge pieces to their proper location. (See for a similar method, the page
Solving Rubik's Cubes: All
Corners Last.) The two algorithms I constructed are one for flipping two
edge pieces: R'UF'U'FU'RU and one for moving moving three edge pieces:
R'U'RUR'URU'RUR'U'. Afterwards, I asked him if he had discovered this himself
and he told me he got it from a YouTube video. I spend some time searching for
that video. I think it is the video:
A simple trick to crack
all Rubik's cubes. For another description, see also: Commutators: corner twists. I also found some interesting video by Dmitry
Zaytsev: Rubik's Cube
3x3. Edges First Method , No algorithms, no notation. Part 1,
Part 2, and
Part 3.
This months interesting links
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Wednesday, December 6, 2017