Re: psychoceramics: 6bar6code6

[acb @ cs.monash.edu.au (Andrew C. Bulhak)]

[Anton Sherwood]
> 
> 
> Learn something new every day!
> 
> Michael Moroney explained:
> : The UPC on consumer products has a bar code such that each digit 0-9 is
> : represented by 4 bars, two light and two dark bars alternating.  Each digit
> : is 7 times the width of the narrowest bar's width and each bar can be 1, 2,
> : 3 or 4 times this width. Additionally there are two possible code for each
> : digit, with each code the "negative" of each other (light and dark reversed).
> 
> Oh, that's cute.  In other words, within the 7 units are six points 
> for a possible edge, exactly three of which must be edges.  (Every 
> fourth edge in a block is mere formatting.)  That means there are 
> twenty possible codes (6!/3!3!):
> 		---|||		|||---
> 		--|-||		||-|--
> 		--||-|		|-||--
> 		--|||-		-|||--
> 		-|--||		||--|-
> 		-|-|-|		|-|-|-
> 		-|-||-		-||-|-
> 		-||--|		|--||-
> 		|---||		||---|
> 		|--|-|		|-|--|
> where `|' is an edge and `-' is a non-edge.  So if a code appears invalid, 
> it is backward; and that tells the reader which digit goes first, without 
> needing an asymmetrical frame.  How elegant!
> 
> (I tried to reverse-engineer the actual code assignments, but my eye
> keeps going out of phase.  Could some weisenheimer have deliberately
> assigned `6' to the code that most resembles the frame-bars?)

Probably not; since each digit differs from the preceding one by only one
position, this looks like a Gray code of some sort...

 -- acb [what the Grays are doing with barcodes I have no idea...]

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