Decomposed Function Cardinality of Selected Logistic Functions.

摘要

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 Lyapunov 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 Lyapunov Exponent, a common measure of complexity in chaotic functions, and then computed the correlation between DFC and the Lyapunov Exponent over all functions.