mosaics from text

I haven't done new mosaics in a while but I had the idea to try images of text. I used a tiny, old, english-language bible for this mosaic, sorting "darkness" from left to right. This one is from an old, german-language art dictionary I picked up at a yard sale years ago.

More mosaics here and <a href=https://www.flickr.com/photos/31382652@N00/albums/72157684474997934/">here.

another dice problem

I added another problem and solution to my dice collection. It's problem 77.

Here's the problem statement: "Suppose we play a game with a die. We roll once, and this first roll is the score. We may continue to roll and add to the score, but if the roll ever divides the score we start with (e.g., if our score is 15 and we roll a 1, 3, or 5), then we lose everything and end up with nothing. If instead we choose to stop, we win an amount proportional to the score. What strategy will yield the maximum expected value of our final score?"

This is an optimal stopping problem. I've been interested in optimal stopping problems for quite a while, as a result of these dice problems and other things. However, I haven't found a really good introductory text to the general theory of optimal stopping that really appeals to me, so I end up doing things rather "from scratch" whenever I solve such problems. I feel like I might be missing some useful tools, but I'm not sure that is the case for the simple problems I'm solving.

nails

A few years ago, I was walking around my neighborhood and came across some items marked "free" on the sidewalk. One of the items was a nice, old tricycle that I thought would be perfect for my friend's daughter. There was also a beautiful old pail full of nails (and a few screws). I put the pail on the tricycle and pushed it all back to my house. The pail then sat in my garage until the other day, I was taking apart an old electric toothbrush and found the strong magnet that most electric toothbrushes seem to contain. I threw this in the pail, and when I pulled it out, it brought a nice clump of nails with it. Doing this 100+ times and photographing each clump resulted in this image.

the logistic map, audio version

I've been making audio versions of the logistic map. The idea I'm using is to create a sound such that its spectrogram looks like the bifurcation diagram of the logistic map. So far I've made two versions.

First version

Second version

The second version is lower in pitch, has panning according to pitch (lower pitch more left, higher pitch more right), gets louder when there is "more" chaos, and more quickly reaches the first bifurcation.