Based on **this image created by Matt Henderson**, I decided to write something for myself that would explore other possible random walks, although mine are generated in a slightly different way than what Matt did.

Each of these images (which will only appear in Chrome, Safari or Firefox, sorry people still using Internet Explorer) is a visual representation of the first 100, 000 digits of the number where each digit of the number corresponds to a different rotation. They may take a while to calculate, depending on the speed of your computer.

Note that for the last "random walk", I increased the scale significantly over the other random walks so that it made the pattern more obvious.

The links for “phi” points to the image for “e”…

Fixed. Thanks!

Hi David,

Thanks for this!

You might be interested in the work of Fran Aragón Artacho and colleagues in producing walks using digits of pi, e etc., by converting them to base 4 and using the different digits to give the step direction. Apart from being beautiful, it is a powerful technique (I think) for visually identifying randomness in decimal (well, base 4) expansions.

Links:

http://walks.carma.newcastle.edu.au/index.html (main project page)

http://walks.carma.newcastle.edu.au/walks.html (images of walks)

http://walks.carma.newcastle.edu.au/publications.html (link to paper describing the main idea and its applications)

Cheers,

Nathan

The image for 1/7th is surprising! It looks like the spiral pieces that Christopher Danielson makes. Did you try it with any other fractions that have a longer repeating cycle?

Hi Carl,

I don’t remember actually. I do remember choosing 1/7 because the cycle was more likely to be visible. It would be interesting to use something like 123456789/9999999999.

Actually, in the long run it would be nice to be able to allow the user to just enter in a number instead of me needing to hard-code in the numbers.

David