Dmitry Shintyakov

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It takes twice the man to ride half the bike

It takes twice the man to ride half the bike

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This scarf with cellular automaton pattern is seamless: after many steps initial pattern returns to its original state, (flipped, because it is Mobius loop)

Here's another piece from the Bridges 2018 art gallery, a scarf with a cellular automaton pattern by Elisabetta Matsumoto, +Henry Segerman, and Fabienne Serriere. This one looks to be Rule 150. The part that raises this above the level of "just another use of cellular automata to create decorative patterns", though, is that they carried out a search for an initial seed pattern that would return to itself, in reversed form, at the right length to form a nice Möbius-band scarf. So (except possibly for any unevenness in actually fabricating the join) the pattern is seamless.

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Crystals of a rare hexagonal shape.

The compound is a double salt, guanidinium aluminium sulfate hexahydrate:

C(NH2)3Al(SO4)2*6H2O

These are not final crystals, just nice samples obtained during recrystallization of the crude compound. I am going to grow larger samples later.

I learned about this compound from this page: http://www.myttex.net/forum/Thread-Solfato-di-guanidina-e-alluminio-III-esaidrato-Sintesi

The compound is a double salt, guanidinium aluminium sulfate hexahydrate:

C(NH2)3Al(SO4)2*6H2O

These are not final crystals, just nice samples obtained during recrystallization of the crude compound. I am going to grow larger samples later.

I learned about this compound from this page: http://www.myttex.net/forum/Thread-Solfato-di-guanidina-e-alluminio-III-esaidrato-Sintesi

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I prepared this compound for another experiment, but during recrystallization step noticed that it easily forms large crystals, so used part of the solution to grow a single crystal.

The formula is (probably) Na3[Al(C2O4)3]*5H2O

Some sources state that it has 3 molecules of H2O, but it seems to be a mistake due to potassium analog.

It is aluminium analog of sodium ferrioxalate

which has very similar though more vividly colored crystals.

Again, similarly to its ferric sibling, it has high solubility exceeding 50g per 100ml and grows easily, but is not stable on air: after few days of exposure to air, it would lose transparency and turn white. I am currently storing it under a layer of liquid paraffin.

Crystal size is about 4cm along the longest face, growing method was slow evaporation (I rarely have success with other methods), growth time is less than 2 weeks.

To prepare this compound, I dissolved Al metal in NaOH solution, then added stoichiometric amount of oxalic acid and heated while stirring until complete dissolution of precipitate. Total equation is:

2 Al + 6 NaOH + 6 H2C2O4 = 2 Na3[Al(C2O4)3] + 6 H2O + 3 H2(g)

The formula is (probably) Na3[Al(C2O4)3]*5H2O

Some sources state that it has 3 molecules of H2O, but it seems to be a mistake due to potassium analog.

It is aluminium analog of sodium ferrioxalate

which has very similar though more vividly colored crystals.

Again, similarly to its ferric sibling, it has high solubility exceeding 50g per 100ml and grows easily, but is not stable on air: after few days of exposure to air, it would lose transparency and turn white. I am currently storing it under a layer of liquid paraffin.

Crystal size is about 4cm along the longest face, growing method was slow evaporation (I rarely have success with other methods), growth time is less than 2 weeks.

**Preparation**To prepare this compound, I dissolved Al metal in NaOH solution, then added stoichiometric amount of oxalic acid and heated while stirring until complete dissolution of precipitate. Total equation is:

2 Al + 6 NaOH + 6 H2C2O4 = 2 Na3[Al(C2O4)3] + 6 H2O + 3 H2(g)

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A month ago there was a large bicycle parade in my city.

Today I have discovered that someone painted me!

Artist name is Mikhail Bazarov (Михаил Базаров)

Today I have discovered that someone painted me!

Artist name is Mikhail Bazarov (Михаил Базаров)

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Oh, that's clever.

I've got interested in Minkowski geometry recently, after reading Greg Egan's "Dichronauts", but never realized that fractals could have negative dimensions in it.

It is quite obvious in the hindsight though: the more "jagged" the path is, the smaller its total pseudo-length.

I've got interested in Minkowski geometry recently, after reading Greg Egan's "Dichronauts", but never realized that fractals could have negative dimensions in it.

It is quite obvious in the hindsight though: the more "jagged" the path is, the smaller its total pseudo-length.

Here's a funny way to get

If the path length gets longer with increasing resolution then your velocity gets closer to that of light and your elapsed time decreases, this can give a negative dimensional curve:

https://tglad.blogspot.com.au/2017/08/negative-dimensional-curves.html

The pic shows the Minkowski time-like equivalent of a Levy C curve. As the dimension decreases the spatial curve gets noticibly smoother. However, the motion itself isn’t really getting smoother, it is just getting closer to light speed, so you can’t see the variation as easily, but the boosts are actually getting ‘rougher’.

It is interesting that the case where the dimension is 0 also seems to be the case where it is smooth. Is it really two circular arcs in the 0+0D case? Is this significant? Or is it obvious?

**negative fractional dimensions**. We look at time-like curves in 2+1D Minkowski space-time. So using special relativity and looking at the temporal dimension: how much the proper elapsed time scales with temporal resolution. In other words, how much time passes for you as you get closer and closer to approximating the trajectory in question.If the path length gets longer with increasing resolution then your velocity gets closer to that of light and your elapsed time decreases, this can give a negative dimensional curve:

https://tglad.blogspot.com.au/2017/08/negative-dimensional-curves.html

The pic shows the Minkowski time-like equivalent of a Levy C curve. As the dimension decreases the spatial curve gets noticibly smoother. However, the motion itself isn’t really getting smoother, it is just getting closer to light speed, so you can’t see the variation as easily, but the boosts are actually getting ‘rougher’.

It is interesting that the case where the dimension is 0 also seems to be the case where it is smooth. Is it really two circular arcs in the 0+0D case? Is this significant? Or is it obvious?

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A good one.

I spent half of the day and five pages of paper, but solved it without hints. Retrospectively, it was not that hard though.

I spent half of the day and five pages of paper, but solved it without hints. Retrospectively, it was not that hard though.

A problem from the XXVI (1963) Moscow Mathematical Olympiad. A simple Somos sequence

https://www.cut-the-knot.org/arithmetic/algebra/SimpleSomosSequence.shtml

#FigureThat #math #arithmetic

https://www.cut-the-knot.org/arithmetic/algebra/SimpleSomosSequence.shtml

#FigureThat #math #arithmetic

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Take A and B, big square matrix with iid normally distributed complex entries.

Let F(t) = A+0.1*exp(2*pi*i*t)*B

Plot the eigenvalues of F(t) in the complex plane as t varies from 0 to 1 over 4 seconds (roughly).

BTW Note that even though the animation has a period of 4 seconds, the individual points follow paths that often take longer than 4 seconds to close the loop.

Motivated by +Terence Tao and Vu: https://projecteuclid.org/euclid.acta/1485892530

Let F(t) = A+0.1*exp(2*pi*i*t)*B

Plot the eigenvalues of F(t) in the complex plane as t varies from 0 to 1 over 4 seconds (roughly).

BTW Note that even though the animation has a period of 4 seconds, the individual points follow paths that often take longer than 4 seconds to close the loop.

Motivated by +Terence Tao and Vu: https://projecteuclid.org/euclid.acta/1485892530

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Crystals of lithium ferric EDTA, a lithium analog of this compound: https://photos.app.goo.gl/iTWDMDqw531YZrFg2

I obtained these crystals experimentally and have no literature references.

The formula is Li[Fe(edta)], where edta stands for ethylenediaminetetraacetate ligand.

Compared to the sodium analog, lithium compound has the same dark brown color, but crystal shape is very different, crystals being almost cubic. Solubility is significantly higher, around 51 g/100ml at room temperature.

Crystals are stable on air.

Preparation: take 1 mol of EDTA acid suspended in water (it has low solubility), add 1 mol of LiOH, then 1 mol of Fe(OH)3 and heat with stirring until complete dissolution of solids.

I obtained these crystals experimentally and have no literature references.

The formula is Li[Fe(edta)], where edta stands for ethylenediaminetetraacetate ligand.

Compared to the sodium analog, lithium compound has the same dark brown color, but crystal shape is very different, crystals being almost cubic. Solubility is significantly higher, around 51 g/100ml at room temperature.

Crystals are stable on air.

Preparation: take 1 mol of EDTA acid suspended in water (it has low solubility), add 1 mol of LiOH, then 1 mol of Fe(OH)3 and heat with stirring until complete dissolution of solids.

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In case you haven't heard it yet: first elementary knightship just discovered in Game of Life.

Here is a link to see it in action: http://catagolue.appspot.com/object/xq6_yyocxukcy6gocs20h0a38bac2qq73uszyjo4w8y0e4mo0vu0o606s6444u08clav0h03g440qq1333333x11zy9ecec2ik032i210sw3f0hy011w70401011033547442zy0emj896he1e1kif6q2gc50ew9qb30dzgo403gg066m32w11z34407q441n6zy311/b3s23

Here is a link to see it in action: http://catagolue.appspot.com/object/xq6_yyocxukcy6gocs20h0a38bac2qq73uszyjo4w8y0e4mo0vu0o606s6444u08clav0h03g440qq1333333x11zy9ecec2ik032i210sw3f0hy011w70401011033547442zy0emj896he1e1kif6q2gc50ew9qb30dzgo403gg066m32w11z34407q441n6zy311/b3s23

Here's an elementary knightship in Conway's Game of Life (that is, a pattern that moves with the slope of a chess knight, and isn't one of the arbitrarily tweakable engineered families). Just discovered.

http://conwaylife.com/forums/viewtopic.php?f=2&t=3303

Via +Richard Holmes.

http://conwaylife.com/forums/viewtopic.php?f=2&t=3303

Via +Richard Holmes.

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Crystals of lithium sulfate, Li2SO4*H2O.

As always, grown using slow evaporation method, rather slowly: growth took whole month.

They are stable on air.

As always, grown using slow evaporation method, rather slowly: growth took whole month.

They are stable on air.

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