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One iteration of the middle-square method, showing a 6-digit seed, which is then squared, and the resulting value has its middle 6 digits as the output value (and also as the next seed for the sequence). Directed graph of all 100 2-digit pseudorandom numbers obtained using the middle-square method with n = 2.
An early computer-based PRNG, suggested by John von Neumann in 1946, is known as the middle-square method. The algorithm is as follows: take any number, square it, remove the middle digits of the resulting number as the "random number", then use that number as the seed for the next iteration.
Middle-Square Weyl Sequence RNG (see also middle-square method) 2017 B. Widynski [34] [35] A variation on John von Neumann's original middle-square method, this generator may be the fastest RNG that passes all the statistical tests. xorshiftr+: 2018 U. C. Çabuk, Ö. Aydın, and G. Dalkılıç [36] A modification of xorshift+.
Dice are an example of a mechanical hardware random number generator. When a cubical die is rolled, a random number from 1 to 6 is obtained. Random number generation is a process by which, often by means of a random number generator (RNG), a sequence of numbers or symbols is generated that cannot be reasonably predicted better than by random chance.
Each row shows the state evolving until it repeats. The top row shows a generator with m = 9, a = 2, c = 0, and a seed of 1, which produces a cycle of length 6. The second row is the same generator with a seed of 3, which produces a cycle of length 2. Using a = 4 and c = 1 (bottom row) gives a cycle length of 9 with any seed in [0, 8].
A mid-squares hash code is produced by squaring the input and extracting an appropriate number of middle digits or bits. For example, if the input is 123 456 789 and the hash table size 10 000, then squaring the key produces 15 241 578 750 190 521, so the hash code is taken as the middle 4 digits of the 17-digit number (ignoring the high digit ...
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Let be a metric space with distance function .Let be a set of indices and let () be a tuple (indexed collection) of nonempty subsets (the sites) in the space .The Voronoi cell, or Voronoi region, , associated with the site is the set of all points in whose distance to is not greater than their distance to the other sites , where is any index different from .