Are there good resources for the distribution of digits in irrational numbers or should I write my own programs, I would think float errors will be a problem.
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closed as not a real question by Scott Morrison♦ Dec 6 at 8:59 |
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The numbers that John D. Cook mentioned are called Normal numbers there are lots of good references at the wikipedia article about them. |
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If you pick a real number from any finite interval, with probability 1 the digits in its decimal expansion are uniformly distributed. In fact, the "digits" are uniformly distributed with respect to any base, not just base 10. It's possible to construct irrational numbers that do not have this property, but so far no one has demonstrated a "natural" number with this property. That is, the numbers have been especially constructed and not numbers that you might otherwise run across, such as pi, for example. |
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Here is an article about the distribution of digits of irrational numbers. From the abstract: "In this study, for quantifying and comparing the complexity of the digits of irrational numbers, we used the first one million digits to calculate the fractal dimensions of the digits of 10 irrational numbers with long sequence of known digits via box-counting algorithm." Fractal and statistical analysis on digits of irrational numbers Dejian Laiand Marius-F. Dancac Chaos, Solitons & Fractals Volume 36, Issue 2, April 2008, Pages 246-252 |
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