Extensiveness Analysis
The extensiveness analysis is based on sequences of analytical properties of many different token sequences of the same kind (based on the chosen alphabet and the number of digits). She describes that for these property sequences no (non-trivial) analytical (meta-)properties or any stochastic patterns can be found. Again, these meta-patterns are neither fully nor partially reproducible or predictable.
The extensiveness of many different token sequences of the same kind for given alphabets is demonstrated here in a visual way using patterns found in (meta-)property sequences and their analytic transformations.
The extensiveness indicators used here are the walk dives, rises and stays. A dive is defined here as a waypoint with a higher predecessor neighbor and a lower successor neighbor. A rise is defined here inversely. A stay is defined here as a waypoint with neighbors of the same kind, both higher or lower.
A word about the peculiarity of the walk dives and rises of DICE tokens: 7,776 is the maximum possible number of the tokens, based on the alphabet ⚀⚁⚂⚃⚄⚅ and the number of 5 digits. Therefore, every DICE walk reaches zero in the end here.
Analysis Archives
DICE - Extensiveness Analysis Archive (9.2 MB)
UPPER_EPCG30 - Extensiveness Analysis Archive (47.1 MB)
TRUE_RANDOM - Extensiveness Analysis Archive (6.4 MB)
MERSENNE_TWISTER - Extensiveness Analysis Archive (6.5 MB)
The linked archives contain
- some metrics of the tokens, of the scores and of the deltas as JSON¹
- the token data, the score and delta numbers as CSV
- the score walk and the walk dives, rises and stays numbers as CSV
- all available plots as shown below as an example in PNG format
¹ only if the data weren't pseudo-randoms or physically generated randoms
Analysis Plots
The aim of the extensiveness plots is to show that the patterns found in (meta-)property sequences of numerical mappings of many token sequences (100 here to be specific) of the same kind, obtained via the Unique Tokens API, cannot be distinguished from patterns found in (meta-)property sequences of numeric pseudo-randoms (MERSENNE_TWISTER) or physically generated numeric randoms (TRUE_RANDOM). The latter are numbers chosen at random from the given integer range without respecting uniqueness, i.e., they do not represent tokens and therefore should presents even less structural patterns.
Walk Dives Plots
The plot shows as example for the DICE alphabet 100 walk dives from 7,776 scores each.
Walk Rises Plots
The plot shows as example for the DICE alphabet 100 walk rises from 7,776 scores each.
Walk Stays Plots
The plot shows as example for the DICE alphabet 100 walk stays from 7,776 scores each.
