Complextropy is an information theoretical quantity defined as the length of the shortest computer program that describes a set S of which x is a βrandomβ or βgenericβ member, factoring in computational resource bounds. It is intended to be a measure of "sophistication" that ignores the contribution of arbitrary or random bits to Kolmogorov complexity.
ββββββββββββββ COMPLEXTROPY ANALYZER ββββββββββββββββββ
β Measuring Structured Complexity vs Random Noise β
βββββββββββββββββββββββββββββββββββββββββββββββββββ
β β
β Input Analysis: β
β ββββββββββββββββββββββββββββββββββββββββ β
β β Sample x: "101011010110" β β
β β β β
β β Total Length: 12 bits β β
β β Pattern Bits: 4 bits β β
β β Random Bits: 8 bits β β
β ββββββββββββββββββββββββββββββββββββββββ β
β β
β Program Length Decomposition: β
β ββββββββββββββββββββββββββββββββββββββββ β
β β Kolmogorov Complexity β β
β β βββββββββββββββββββββββ β β
β β Complextropy β β
β β βββββ β β
β β Random Noise β β
β β ββββββββββββββ β β
β ββββββββββββββββββββββββββββββββββββββββ β
β β
β Set Membership Analysis: β
β ββββββββββββββββββββββββββββββββββββββββ β
β β Set S = {strings with pattern "1*0*"} β β
β β β β
β β xβ: 10101101 β β
β β xβ: 10110110 β Sample x β β
β β xβ: 11010101 β β
β β ... β β
β ββββββββββββββββββββββββββββββββββββββββ β
β β
β Resource-Bounded Computation: β
β ββββββββββββββββββββββββββββββββββββββββ β
β β Time: O(nΒ²) Space: O(n) β β
β β βββββββ βββββββ βββββββ β β
β β βInputβ β> βProc.β β> βOutputβ β β
β β βββββββ βββββββ βββββββ β β
β ββββββββββββββββββββββββββββββββββββββββ β
β β
β Complexity Spectrum: β
β ββββββββββββββββββββββββββββββββββββββββ β
β β Low Medium High β β
β β βββ βββ βββ β β
β β Random Structured Complex β β
β ββββββββββββββββββββββββββββββββββββββββ β
β β
β [Calculate] [Analyze Pattern] [Compare Samples] β
ββββββββββββββββββββββββββββββββββββββββββββββββββββββ