Pair Entropy Data for Long Numbers

Citation Author(s):
William
Julius
Submitted by:
William Julius
Last updated:
Tue, 01/23/2024 - 12:23
DOI:
10.21227/9pp4-1297
Data Format:
pxp, CSV
License:
Creative Commons Attribution
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Categories:
Other
Keywords:
irrational numbers, entropy, pair entropy, random numbers
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Abstract 

Here we analyze the pair entropy function on large numbers by generating sets of pseudo-random numbers and calculating the pair entropy as a function of number of digits. We analyze the statistical behavior of the average entropy, determine that the average entropy grows logarithmically in the asymptotic limit, and discuss the behavior of higher statistical moments. We observe several distinct regions emerge with transitions that depend on the base of the numbers considered.

Instructions: 

Pair entropy calculations per digit on pseudo random numbers. Two different runs of 1000 (25000 numbers) and 10000 (250 numbers) are done for both single digits and total entropy in three different bases (2,10,26). Raw entropy calculations as well as the igor files used to plot are included.

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