A Million Arbitrary Digits

With a thousand appetizers …

Back before researchers and programmers had easy access to random (or pseudo-random) numbers, organizations would publish tables of random digits. One important one was done by the RAND Corporation: A Million Random Digits with 100,000 Normal Deviates. It listed the random digits in groups of 5, 10 groups (=50 digits) per line.

Since I’ve been generating arbitrary numbers from images, I thought it would be appropriate to make available a million arbitrary digits (that’s an uncompressed tab-delimited file). They were generated from the usual image, using the luminance property, with a sampling rate of 71.

While a million digits is too many to show, below are the first 1,000 to give you a taste. Below that list is some more information about the distribution of the digits.

Here’s some information about the distribution of the digits, both statistics and visualized.

While it’s not surprising that the distribution of digits isn’t uniform, it is striking just how few occurrences there are of 0 and especially of 9.

Single digits aren’t necessarily that useful, so we might take pairs of consecutive digits to form numbers between 0 and 100. So a 3 followed by a 4 would become 34. Given that the digits are skewed, the two digit numbers will be skewed as well. Here’s what their distribution looks like:

The overall distribution is roughly (though not exactly) replicated at each decade, which makes sense.

Anyway, useful? Stay tuned …