Decomposed Function Cardinality of Selected Logistic Functions
WRIGHT LAB WRIGHT-PATTERSON AFB OH
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This report documents an experiment in decomposing logistic functions a set of functions which belong to the class of chaotic functions and correlating their Decomposed Function Cardinality DFC with their Lyaponov exponent. This memo documents the results of Pattern Theory 2 Task Order 3. The objective of this task was to decompose a set of logistic functions. In our prior experiments into the phenomonology of function decomposition reported on in Pattern Theory An Engineering Paradigm For Algorithm Design WL-TR-91-1060 we decomposed a wide variety of non-chaotic functions. The logistics functions decomposed in this task represent our first look at the ability of decomposed function cardinality DFC to measure complexity or patternness in a chaotic function. For each logistic function that we decomposed, we also calculated an approximation of the Lyaponov Exponent, a common measure of complexity in chaotic functions, and then computed the correlation between DFC and the Lyaponov Exponent over all functions.
- Theoretical Mathematics