Thanks for the assertion and the correction. I knew it was named after a person, hence the upper case G, but I am one of those that reads and writes phonetically (if you know what I mean) and I could not see (hear) the difference between Gray and grey.
On Sun, Nov 17, 2013 at 12:06 PM, Henry Rich <[email protected]> wrote: > Oh - and it's Gray code, not Grey. It's named not because you don't have > black-to-white transitions on more than one bit at a time; it's named for > Frank Gray. > > > Henry Rich > > On 11/17/2013 11:24 AM, Jose Mario Quintana wrote: > >> My understanding is that Grey codes encode numbers in such a way that the >> binary representation of consecutive numbers (including the last and first >> couple) in the sequence can be produced, one from the other, by flipping >> only one bit. >> For example, the binary representation of a four bit Grey sequence, of 2^4 >> numbers, and the flipping bit to produce the next number follows, >> >> o=. @: >> ( Grey=. (xor f. <. o -:) o i. o (2&^)) ( xor=. 22 b. ) >> (22 b. <.@:-:)@:i.@:(2&^) 22 b. >> >> (#: ; (2 #: o (xor/\) ]) o (, {.)) o Grey 4 >> ┌───────┬───────┐ >> │0 0 0 0│0 0 0 1│ >> │0 0 0 1│0 0 1 0│ >> │0 0 1 1│0 0 0 1│ >> │0 0 1 0│0 1 0 0│ >> │0 1 1 0│0 0 0 1│ >> │0 1 1 1│0 0 1 0│ >> │0 1 0 1│0 0 0 1│ >> │0 1 0 0│1 0 0 0│ >> │1 1 0 0│0 0 0 1│ >> │1 1 0 1│0 0 1 0│ >> │1 1 1 1│0 0 0 1│ >> │1 1 1 0│0 1 0 0│ >> │1 0 1 0│0 0 0 1│ >> │1 0 1 1│0 0 1 0│ >> │1 0 0 1│0 0 0 1│ >> │1 0 0 0│1 0 0 0│ >> └───────┴───────┘ >> >> However, flipping as many as three bits are sometimes required for the >> referred sequence, >> >> T=. 0 8 12 14 15 13 10 11 9 4 6 7 5 2 3 1 >> >> (#: ; (2 #: o (xor/\) ]) o (, {.)) T >> ┌───────┬───────┐ >> │0 0 0 0│1 0 0 0│ >> │1 0 0 0│0 1 0 0│ >> │1 1 0 0│0 0 1 0│ >> │1 1 1 0│0 0 0 1│ >> │1 1 1 1│0 0 1 0│ >> │1 1 0 1│0 1 1 1│ >> │1 0 1 0│0 0 0 1│ >> │1 0 1 1│0 0 1 0│ >> │1 0 0 1│1 1 0 1│ >> │0 1 0 0│0 0 1 0│ >> │0 1 1 0│0 0 0 1│ >> │0 1 1 1│0 0 1 0│ >> │0 1 0 1│0 1 1 1│ >> │0 0 1 0│0 0 0 1│ >> │0 0 1 1│0 0 1 0│ >> │0 0 0 1│0 0 0 1│ >> └───────┴───────┘ >> >> Am I missing something? >> >> >> >> On Fri, Nov 15, 2013 at 2:07 PM, R.E. Boss <[email protected]> wrote: >> >> Actually, it IS a (4D binary reflected) Gray code. >>> >>> >>> R.E. Boss >>> >>> (Add your info to http://www.jsoftware.com/jwiki/Community/Demographics) >>> >>> >>> -----Original Message----- >>>> From: [email protected] [mailto:programming- >>>> [email protected]] On Behalf Of Devon McCormick >>>> Sent: vrijdag 15 november 2013 19:33 >>>> To: J-programming forum >>>> Subject: Re: [Jprogramming] Sets >>>> >>>> These look like Gray codes. >>>> >>>> On Nov 14, 2013 10:04 PM, "Raul Miller" <[email protected]> wrote: >>>> >>>>> >>>>> Easy enough to add. >>>>> >>>>> It's an interesting progression though: >>>>> >>>>> #:/:&> (<@#~ 2 #:@i.@^ #)&.> set 2;'b';1;'a' >>>>> 0 0 0 0 >>>>> 1 0 0 0 >>>>> 1 1 0 0 >>>>> 1 1 1 0 >>>>> 1 1 1 1 >>>>> 1 1 0 1 >>>>> 1 0 1 0 >>>>> 1 0 1 1 >>>>> 1 0 0 1 >>>>> 0 1 0 0 >>>>> 0 1 1 0 >>>>> 0 1 1 1 >>>>> 0 1 0 1 >>>>> 0 0 1 0 >>>>> 0 0 1 1 >>>>> 0 0 0 1 >>>>> >>>>> -- >>>>> Raul >>>>> >>>>> On Thu, Nov 14, 2013 at 6:06 PM, km <[email protected]> wrote: >>>>> >>>>>> Cool; needs a sort. --Kip >>>>>> >>>>>> >>>>>> psr=: (<@#~ 2 #:@i.@^ #)&.> NB. Raul's >>>>>> psr set 0;1 >>>>>> +----------------+ >>>>>> |++---+---+-----+| >>>>>> |||+-+|+-+|+-+-+|| >>>>>> ||||1|||0|||0|1||| >>>>>> |||+-+|+-+|+-+-+|| >>>>>> |++---+---+-----+| >>>>>> +----------------+ >>>>>> ps set 0;1 NB. list inside box is sorted >>>>>> +----------------+ >>>>>> |++---+-----+---+| >>>>>> |||+-+|+-+-+|+-+|| >>>>>> ||||0|||0|1|||1||| >>>>>> |||+-+|+-+-+|+-+|| >>>>>> |++---+-----+---+| >>>>>> +----------------+ >>>>>> >>>>>> Sent from my iPad >>>>>> >>>>>> On Nov 14, 2013, at 3:17 PM, Raul Miller <[email protected]> >>>>>>> >>>>>> wrote: >>>> >>>>> >>>>>>> Derived from ps at http://rosettacode.org/wiki/Power_set#J >>>>>>> >>>>>>> ps=: (<@#~ 2 #:@i.@^ #)&.> >>>>>>> >>>>>>> -- >>>>>>> Raul >>>>>>> >>>>>>> >>>>>>> On Thu, Nov 14, 2013 at 3:17 PM, km <[email protected]> wrote: >>>>>>>> Here is my latest attempt at sets in J. Would anyone care to write >>>>>>>> >>>>>>> a >>> >>>> verb ps (power set) such that ps y is the set of all subsets of set y? >>>> It's called the power set in part because when a set has n elements >>>> its >>>> power set has 2^n elements. --Kip Murray >>>> >>>>> >>>>>>>> NB. A set is a box with a sorted list of boxes inside. >>>>>>>> NB. An element is the contents of a box in the list. >>>>>>>> NB. A -: B tests whether set A is set B. >>>>>>>> >>>>>>>> set =: [: < [: /:~ ~. NB. create set from list of boxes >>>>>>>> >>>>>>>> NB. The list may have duplicates but the set has none. >>>>>>>> >>>>>>>> EE =: <$0 NB. empty set, same as Ace a: >>>>>>>> >>>>>>>> eo =: <@[ e. >@] NB. test whether x is an element of y >>>>>>>> >>>>>>>> uu =: [: set ,&> NB. union >>>>>>>> >>>>>>>> mm =: [: < -.&> NB. minus >>>>>>>> >>>>>>>> sd =: mm uu mm~ NB. symmetric difference >>>>>>>> >>>>>>>> cp =: uu mm sd NB. common part (intersection) >>>>>>>> >>>>>>>> ss =: uu -: ] NB. test whether x is a subset of y >>>>>>>> >>>>>>>> (set 1;2;3;3) -: set 3;1;2 >>>>>>>> 1 >>>>>>>> >>>>>>>> ]A =: set 2;'b';1;'a' >>>>>>>> +---------+ >>>>>>>> |+-+-+-+-+| >>>>>>>> ||1|2|a|b|| >>>>>>>> |+-+-+-+-+| >>>>>>>> +---------+ >>>>>>>> >>>>>>>> ]B =: set 'b';'a';4;3;'a' >>>>>>>> +---------+ >>>>>>>> |+-+-+-+-+| >>>>>>>> ||3|4|a|b|| >>>>>>>> |+-+-+-+-+| >>>>>>>> +---------+ >>>>>>>> >>>>>>>> A uu B >>>>>>>> +-------------+ >>>>>>>> |+-+-+-+-+-+-+| >>>>>>>> ||1|2|3|4|a|b|| >>>>>>>> |+-+-+-+-+-+-+| >>>>>>>> +-------------+ >>>>>>>> >>>>>>>> A sd B >>>>>>>> +---------+ >>>>>>>> |+-+-+-+-+| >>>>>>>> ||1|2|3|4|| >>>>>>>> |+-+-+-+-+| >>>>>>>> +---------+ >>>>>>>> >>>>>>>> A cp B >>>>>>>> +-----+ >>>>>>>> |+-+-+| >>>>>>>> ||a|b|| >>>>>>>> |+-+-+| >>>>>>>> +-----+ >>>>>>>> >>>>>>>> NB. Below is the set of all subsets of set 0;1 >>>>>>>> >>>>>>>> set EE;(set <0);(set <1);<set 0;1 >>>>>>>> +------------------------+ >>>>>>>> |+--+-----+-------+-----+| >>>>>>>> ||++|+---+|+-----+|+---+|| >>>>>>>> ||||||+-+|||+-+-+|||+-+||| >>>>>>>> ||++|||0|||||0|1|||||1|||| >>>>>>>> || ||+-+|||+-+-+|||+-+||| >>>>>>>> || |+---+|+-----+|+---+|| >>>>>>>> |+--+-----+-------+-----+| >>>>>>>> +------------------------+ >>>>>>>> >>>>>>>> Sent from my iPad >>>>>>>> >>>>>>>> ------------------------------------------------------------ >>> ---------- >>> >>>> For information about J forums see >>>>>>>> >>>>>>> http://www.jsoftware.com/forums.htm >>>> >>>>> >>>>>>> ------------------------------------------------------------ >>> ---------- >>> >>>> For information about J forums see >>>>>>> >>>>>> http://www.jsoftware.com/forums.htm >>>> >>>>> >>>>>> ------------------------------------------------------------ >>> ---------- >>> >>>> For information about J forums see >>>>>> >>>>> http://www.jsoftware.com/forums.htm >>>> >>>>> ---------------------------------------------------------------------- >>>>> For information about J forums see >>>>> >>>> http://www.jsoftware.com/forums.htm >>>> ---------------------------------------------------------------------- >>>> For information about J forums see http://www.jsoftware.com/forums.htm >>>> >>> >>> ---------------------------------------------------------------------- >>> For information about J forums see http://www.jsoftware.com/forums.htm >>> >>> ---------------------------------------------------------------------- >> For information about J forums see http://www.jsoftware.com/forums.htm >> >> ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
