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Computational Complexity of the Logistic Map

This Demonstration shows the computational space complexity needed to exactly compute the iteration of the logistic equation ). The initial value of the iteration is , with , the number of iterations performed, and , the bifurcation parameter for the logistic map. Each value of the orbit, , is computed up to relative error of .

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Computational space complexity is measured as "loss of precision rate" , where is the mantissa length needed to represent the initial value such that the precision requirement—relative error less than or equal to for all —is fulfilled. The blue curve shows the "exact" orbit computed this way. The red curve shows the orbit computed with machine precision. For more information, see the article C. Spandl, "Computational Complexity of Iterated Maps on the Interval," Electronic Proceedings in Theoretical Computer Science, 24 (http://arxiv.org/html/1006.0551), 2010 pp. 139–150.
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