We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The BiEntropy algorithm evaluates the order and disorder within and across an entire binary string of length n in O(n^2)time using O(n) memory. The algorithm uses a weighted average of the Shannon Entropies of the string and the first n-2 binary derivatives of the string. We successfully test the algorithm in the fields of  Human Vision, Cryptography, Random Number Generation and Quantitative Finance.
We design, implement and test a simple algorithm which computes the approximate entropy of a finite binary string of arbitrary length. The algorithm uses a weighted average of the Shannon Entropies of the string and all but the last binary derivative of the string. We successfully test the algorithm in the fields of Prime Number Theory (where we prove explicitly that the sequence of prime numbers is not periodic), Human Vision, Cryptography, Random Number Generation and Quantitative Finance.
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BiEntropy algorithm evaluates the order and disorder within and across an entire binary string of length n in O(n^2)time using O(n) memory. The algorithm
algorithm
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the first n-2 binary derivatives
all but the last binary derivative
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Prime Number Theory (where we prove explicitly that the sequence of prime numbers is not periodic),