Thursday, September 27, 2012

Printable Wall Calendar For 2013

Photos of a wall calendar for 2013.

Time for printing a new wall calendar for the coming year 2013. This one is similar to the one for 2012 - I made the days a bit bigger, and interwove the months to a continuous flow of days, to save some space. To identify the months, I gave each month its own color. Not sure how happy I am with these changes, but I'll just have to try it in real life and see what improvements I can come up with for 2014...

The calendar is on two pages, with January to June on the first and the rest on the second. The weeks begin with Mondays. Weekends are marked by a less bright white than the week days.

Download the pdf and print it on a regular printer. (The Google Docs viewer doesn't seem to understand transparency, so it doesn't show the month names or the weekend day boxes, but they'll be there when you print.)

The calendar is made in Inkscape, my favorite free vector graphics editor. The correct date/weekday arrangement for 2013 comes from Inkscape's Extensions -> Render -> Calendar function.

Monday, September 24, 2012

Emulsion separation time lapse

Fluid turbulence in a bottle of hairspray. Johanna bought a bottle of hair spray, consisting of two fluids, a clear and a white one. The product. The spray should be shaken before using, so that the two fluids mix. Above are some snapshots of turbulence achieved by gently shaking the bottle.

After a while, if left alone, the two fluids separate again. We've been quite fascinated by the mixing and re-separation processes.

This is a time lapse video of the hair spray, taken after shaking the bottle. The video starts with the emulsion completely white, that is, with the two solutions mixed. The whole separation process in the video takes about twenty hours.

From each frame in the video I cut a narrow vertical slice, always at the same position in the frame - this is apparently known as 'time slicing'. When these slices are placed beside each other a picture new is formed, where the horizontal direction represents time.

Three regions with different behavior can be seen in the picture. Here exponential curves have been fitted to the interface between the two fluids, in order to find the time constants. I expected to find a simple exponential time dependence, based on a vaguely remembered chemistry demonstration, but the result turned out to be more complex. When I searched for some explanation, I could only find complicated theories for how foams drain (pdf), and no mention of the simple exponential behavior.

Sunday, September 16, 2012

Decagon Girih Solutions

In an earlier post, I wrote about two solutions for the pattern on the ten-sided Girih tile.

In the middle is the standard one, also in paper in Science. The one on the right, with straight lines, I saw in a post on Robodino about laser cutting Girih tiles. The one on the left I might have seen somewhere, or made up myself... Anyway, these are three different solutions with tenfold rotational symmetry.

Wikipedia says: "Most tiles have a unique pattern of girih inside the tile which are continuous and follow the symmetry of the tile. However, the decagon has two possible girih patterns one of which has only fivefold rather than tenfold rotational symmetry." - but it doesn't say which ones they mean.

After some playing around, I realized that there are all kinds of ways to connect the patterns while still (I think) following the rules. The ones above have only a twofold rotational symmetry. These are probably not the only ones, but with their low symmetry, they are not the most interesting...

Instead, I'm really happy about these! They all have fivefold rotational symmetry. The upper left one is the one we cut in acrylic, and the rest are new. The lower left one might not quite conform, since it has another type of crossing in the middle, but who cares? It's pretty!

All in all, these are eleven possible girih patterns for the decagon. Could Wikipedia be wrong on this?

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