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- Middle-square_method abstract "In mathematics, the middle-square method is a method of generating pseudorandom numbers. In practice it is not a good method, since its period is usually very short and it has some severe weaknesses, such as the output sequence almost always converging to zero.The method was first described in a manuscript by a Franciscan friar known only as Brother Edvin sometime between 1240 and 1250. It was reinvented by John von Neumann, and was described at a conference in 1949.To generate a sequence of 4-digit pseudorandom numbers, a 4-digit starting value is created and squared, producing an 8-digit number. If the result is less than 8 digits, leading zeroes are added to compensate. The middle 4 digits of the result would be the next number in the sequence, and returned as the result. This process is then repeated to generate more numbers.For a generator of n-digit numbers, the period can be no longer than 8n. If the middle 4 digits are all zeroes, the generator then outputs zeroes forever. If the first half of a number in the sequence is zeroes, the subsequent numbers will be decreasing to zero. While these runs of zero are easy to detect, they occur too frequently for this method to be of practical use. The middle-squared method can also get stuck on a number other than zero. For n = 4, this occurs with the values 0100, 2500, 3792, and 7600. Other seed values form very short repeating cycles, e.g., 0540 → 2916 → 5030 → 3009. These phenomena are even more obvious when n = 2, as none of the 100 possible seeds generates more than 14 iterations without reverting to 0, 10, 50, 60, or a 24 ↔ 57 loop.In the 1949 talk, Von Neumann quipped that, \"Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin.\" What he meant, he elaborated, was that there were no true \"random numbers\", just means to produce them, and \"a strict arithmetic procedure\", like the one described above, \"is not such a method\". Nevertheless he found these methods hundreds of times faster than reading \"truly\" random numbers off punch cards, which had practical importance for his ENIAC work. He found the \"destruction\" of middle-square sequences to be a factor in their favor, because it could be easily detected: \"one always fears the appearance of undetected short cycles\". Nicholas Metropolis reported sequences of 750,000 digits before \"destruction\" by means of using 38-bit numbers with the \"middle-square\" method.".
- Middle-square_method thumbnail Middle-square_method.svg?width=300.
- Middle-square_method wikiPageID "753942".
- Middle-square_method wikiPageLength "3938".
- Middle-square_method wikiPageOutDegree "13".
- Middle-square_method wikiPageRevisionID "701057946".
- Middle-square_method wikiPageWikiLink Blum_Blum_Shub.
- Middle-square_method wikiPageWikiLink Category:Pseudorandom_number_generators.
- Middle-square_method wikiPageWikiLink ENIAC.
- Middle-square_method wikiPageWikiLink John_von_Neumann.
- Middle-square_method wikiPageWikiLink Leading_zero.
- Middle-square_method wikiPageWikiLink Linear_congruential_generator.
- Middle-square_method wikiPageWikiLink Mathematics.
- Middle-square_method wikiPageWikiLink Nicholas_Metropolis.
- Middle-square_method wikiPageWikiLink Pseudorandomness.
- Middle-square_method wikiPageWikiLink Punched_card.
- Middle-square_method wikiPageWikiLink Sin.
- Middle-square_method wikiPageWikiLink File:Middle-square_method.svg.
- Middle-square_method wikiPageWikiLink File:Middle_square_method_2_digits.svg.
- Middle-square_method wikiPageWikiLinkText "Middle-square method".
- Middle-square_method wikiPageWikiLinkText "middle-square method".
- Middle-square_method subject Category:Pseudorandom_number_generators.
- Middle-square_method hypernym Method.
- Middle-square_method type Software.
- Middle-square_method type Algorithm.
- Middle-square_method type Generator.
- Middle-square_method type Redirect.
- Middle-square_method type Generator.
- Middle-square_method comment "In mathematics, the middle-square method is a method of generating pseudorandom numbers. In practice it is not a good method, since its period is usually very short and it has some severe weaknesses, such as the output sequence almost always converging to zero.The method was first described in a manuscript by a Franciscan friar known only as Brother Edvin sometime between 1240 and 1250.".
- Middle-square_method label "Middle-square method".
- Middle-square_method sameAs Q466575.
- Middle-square_method sameAs Mittquadratmethode.
- Middle-square_method sameAs Mezo-kvadrata_maniero.
- Middle-square_method sameAs m.038hdk.
- Middle-square_method sameAs Q466575.
- Middle-square_method sameAs 平方取中法.
- Middle-square_method wasDerivedFrom Middle-square_method?oldid=701057946.
- Middle-square_method depiction Middle-square_method.svg.
- Middle-square_method isPrimaryTopicOf Middle-square_method.
