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.

35434 | 53334 | 44314 | 65443 | 33424 | 23332 | 24343 | 33343 | 44355 | 14334 |

54434 | 45243 | 32332 | 33454 | 33533 | 34333 | 63535 | 43435 | 23432 | 33442 |

34433 | 44343 | 22554 | 45333 | 35224 | 32342 | 33436 | 44443 | 43322 | 34454 |

45436 | 33333 | 34443 | 34444 | 64473 | 32524 | 52534 | 35324 | 33332 | 23467 |

54334 | 42333 | 35544 | 44445 | 33313 | 35345 | 44442 | 33362 | 24655 | 43534 |

34334 | 33332 | 42347 | 74534 | 42234 | 33635 | 33352 | 23313 | 44333 | 54432 |

54362 | 24553 | 53425 | 33334 | 23242 | 43347 | 54423 | 46334 | 24334 | 33332 |

35323 | 32333 | 64533 | 44333 | 24433 | 54335 | 33334 | 33334 | 44242 | 44433 |

33223 | 37333 | 43443 | 35323 | 32234 | 64534 | 42423 | 24334 | 55534 | 34234 |

23354 | 33344 | 44644 | 33123 | 34315 | 35442 | 36333 | 32323 | 56543 | 43443 |

33447 | 24633 | 45334 | 33353 | 64344 | 44544 | 63226 | 44354 | 25344 | 35343 |

42222 | 44421 | 42433 | 24337 | 37343 | 43433 | 13343 | 45445 | 44443 | 62223 |

35533 | 35355 | 36342 | 43222 | 45622 | 32533 | 23244 | 34343 | 43233 | 23333 |

23554 | 34344 | 52133 | 34333 | 33353 | 36444 | 33222 | 52444 | 33442 | 23332 |

23336 | 43443 | 33352 | 22434 | 44336 | 32232 | 34633 | 53354 | 36343 | 24332 |

42224 | 34232 | 33343 | 23344 | 44363 | 44352 | 22454 | 34124 | 32244 | 35344 |

34464 | 35233 | 54343 | 53533 | 36322 | 23444 | 32253 | 44363 | 43332 | 32364 |

15523 | 12234 | 46243 | 44345 | 44234 | 43344 | 54534 | 33313 | 13346 | 53355 |

44373 | 43333 | 22235 | 24323 | 22432 | 33332 | 44546 | 53234 | 44222 | 53343 |

42323 | 22342 | 63645 | 44364 | 43433 | 23525 | 32133 | 52233 | 33333 | 54537 |

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

Mean | 3.47 |
---|---|

Median | 3 |

Standard deviation | 1.80 |

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 …