# Computational Complexity of the Logistic Map

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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 .

Contributed by: Christoph Spandl (March 2011)
Open content licensed under CC BY-NC-SA

## Details

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.

## Permanent Citation

Christoph Spandl

 Feedback (field required) Email (field required) Name Occupation Organization Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback. Send