## Just what the world needs!

Another maths blog. I am not sure if ‘another’ is entirely appropriate as there are not that many maths blogs, but as there are so many blogs in general maybe it can stand. Basically I have found myself having thoughts recently, its quite disturbing, and as many of them having nowhere to go but run round my head I decided to get rid of some of them in a public (though almost certain totally unread) place. Hence this blog.

The thoughts, and thus the major themes of this blog revolve around mathematics communication and mathematics art. These two will come together naturally as one can use art to communicate mathematics.

I hope to put one piece up a week, I have a few things written that can be polished and exposed, so I should be able to keep that up for a couple of months at least. I might also put up half worked out artistic ideas, but my paranoia might keep those under wraps. I am not sure if that is the paranoia of people thinking my ideas are dull, or the paranoia of people finding them so interesting they nick them. It feels wrong that I have to suffer both.

For starters a small puzzle. It has a real prize! A set of laser cut wooden tiles like those below to the first person who can tell me what the background of the header is. Not the image on the left, thats just a flowsnake [Edit 19/5/12: The original logo is preserved above, the puzzling part was removed in a redesign]

Are you going to write something about Marcus du Sautoy?

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Hi Edmund,

I bet you received the answer to your puzzle long ago, but the header background looks like it was created by recursively applying the fractal Kolakoski sequence, OEIS A000002 (not including the first term, so A078880). The way I saw this was to look at successive rows in the image, and count the number of pixels between light/dark transitions. That counting gave the following sequences, and the Kolakoski sequence jumped out as the second row.

1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,…

2,2,1,1,2,1,2,2,1,2,2,1,1,2,1,1,…

4,2,2,1,4,1,4,2,2,2,4,1,2,2,2,1,… (A088570)

6,3,4,1,6,2,6,3,2,3,6,2,2,3,…

9,5,6,2,9,2,9,4,3…

…

Each successive row is made by summing together elements from the prior row using the Kolakoski sequence (which specifies how many elements to sum together). The first term of row n+1 is the sum of the first

twoterms of row n. The second term of row n+1 is the sum of the subsequenttwoterms of row n. The third term of row n+1 is the subsequentoneof row n, the fourth of row n+1 the subsequentoneof row n, etc.Some further interesting sequences (related to the Kolakoski) that I see in your image are:

First transition point of each row, A042942

1,2,4,6,9,14,22,33,…

The length of the first dark block in successive rows, A111123

1,2,2,3,5,8,11,16,…

The self describing Kolakoski reminded me of sequences detailed in Hofstadter’s book “Fluid Concepts and Creative Analogies”, though I checked and the ones there turned out to be different.

Best,

Roice

You are the first to get all the details, congratulations!

I would rather not part with the tiles originally put up as a prize as I cannot make any more. I can offer a set of Penrose tiles that will be made some time in late January. Send me an email if that sounds interesting!

Congratulations again.

Edmund

Cool blog, total respect for Maxwells Daemon, but dude, you cant keep those tiles you already gave them away.

Its cheeky of me isn’t it! Luckily the person who deserves them is happy with the replacement.