Binary string gradients

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I am working with a program that produces a polydisperse mixture of binary strings. I was wondering if there was some methodology that exists that can measure the 'gradient strength' along each chain, ie, possibly some parameterization that can quantify this for something like 0001111 vs 0010011, vs 0100110111, etc. If you know of something that relates to this or can point me to a journal article which has already done something like this please let me know asap! Thx!
 

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CRGreathouse
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I really don't know what you're asking for, could you give an example? Areyou looking for the difference (in one of various ways) between various strings of bits?
 
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The answer is 011010111000102.
 
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for instance, something like 000011111 vs 000011100111011111. so there some way to calculate something like a numerical gradient of how the bits change? i just wanted to know if there was anyway to quantify something like this.
 
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So you want to know how to find the smoothness of a dither between two colors in one dimension? So 00001111 is a sharp edge, 00010111 is slightly smoother, and 00101011 is even smoother? I don't know of any model of this off the top of my head, but surely many computer graphics programs (like Photoshop, or perhaps even MSPaint) have algorithms programmed in for this.
 

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