Not quite the same:
> (,#;._1)^:(]`1:)5
> 1 0 1 1 0 1 0 1 1 0 1 1 0
This is the start of the infinite fibonacci word (IFW): OEIS A005614
, and
> ;(,,~&.>/@:{.~&_2)^:(4)1;1 0
> 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0
can be found a (infinite) number of times in IFW starting at position 3 (index
2).
Playing a bit:
# IFW=: (,#;._1)^:(]`1:)32
5702887
is the infinite word, then let's mark the positions of
b=.;(,,~&.>/@:{.~&_2)^:(4)1;1 0
I. b E."1 IFW
2 36 57 91 125 146 180 201 235 269 290 324 358 ...
take the first differences
(}.-}:)I. b E."1 IFW
34 21 34 34 21 34 21 34 34 21 34 34 21 34 21 34 34 21 34 21 34 34 21 ...
and reduce them to a bitstring:
(<.@%>./)(}.-}:)I. b E."1 IFW
1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 ...
and back again is the IFW. So 'imploding' IFW by means of marking the
positions of a Turing Google Word (of arbitrary length?) produces IFW again
For the mathematicians among you J-ers perhaps obvious, but certainly
fun for me.
On 25-06-12 14:36, R.E. Boss wrote:
> We had invented this before,
> http://www.jsoftware.com/pipermail/programming/2007-November/008780.html
>
> (,#;._1)^:(]`1:)5
> 1 0 1 1 0 1 0 1 1 0 1 1 0
>
> But the new solution is quite a bit faster and leaner.
>
>
> R.E. Boss
>
>
>> -----Oorspronkelijk bericht-----
>> Van: [email protected] [mailto:[email protected]] Namens
>> Aai
>> Verzonden: maandag 25 juni 2012 13:33
>> Aan: Chat forum
>> Onderwerp: Re: [Jchat] Turing on googol
>>
>> ... and then
>>
>> ;(,,~&.>/@:{.~&_2)^:(4)1;1 0
>> 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0
>>
>> will run (much) faster.
>>
>> On 25-06-12 10:53, I wrote:
>>> Thanks to the analysis of other people, see e.g.
>>> http://mrob.com/pub/math/seq-google-turing.html, it turns out that
>>> fibonacci is involved:
>>>
>>> Using these for generating the bits:
>>>
>>> ;bits=.([:;(-.`(,-.)@.])&.>)&.>^:(<12) <1
>>> 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 ...
>>>
>>> +/&> bits
>>> 1 1 2 3 5 8 13 21 34 55 89 144
>>>
>>>
>>>
>>>
>>>
>>>
>>> On 23-06-12 17:48, Devon McCormick wrote:
>>>> The link says it's spelling out "Google" but I believe that is
>>>> incorrect - it looks like it's just counting up in binary.
>>>>
>>>> On Sat, Jun 23, 2012 at 10:07 AM, Donna Y <[email protected]> wrote:
>>>>> Thanks for the link. I did not watch long enough. Yes it's the
>>>>> code breaker and not an implementation of his first proof. It
>>>>> simply spells out Google.
>>>>>
>>>>> As the video asks, imagine if Alan Turing could work on one of
>>>>> today's computers to expand on any of the many problems he was
>>>>> pursuing!
>>>>>
>>>>> Donna
>>>>> [email protected]
>>>>>
>>>>>
>>>>> On 2012-06-23, at 7:11 AM, Brian Schott <[email protected]> wrote:
>>>>>
>>>>>> Thanks.
>>>>>> Can the working model be saved somehow?
>>>>>> Btw, I found an interesting explanation at
>>>>>> http://news.cnet.com/8301-17852_3-57459126-71/googles-impossibly-clever-alan-turing-doodle/
>>>>>>
>>>>>> That link suggests another purpose of the doodle.
>>>>>>
>>>>>> On Sat, Jun 23, 2012 at 1:26 AM, Donna Y <[email protected]> wrote:
>>>>>>> Its Alan Turing's birthday and that is the proof of the halting
>>>>>>> problem - see Church and Turing.
>>>>>>>
>>>>>>> Donna
>>>>>>> [email protected]
>>>>>>>
>>>>>>>
>>>>>> ----------------------------------------------------------------------
>>>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>>>>
>>>>> ----------------------------------------------------------------------
>>>>> For information about J forums see http://www.jsoftware.com/forums.htm
>>>>
>> --
>> Met vriendelijke groet,
>> @@i = Arie Groeneveld
>>
>>
>>
>> ----------------------------------------------------------------------
>> For information about J forums see http://www.jsoftware.com/forums.htm
> ----------------------------------------------------------------------
> For information about J forums see http://www.jsoftware.com/forums.htm
--
Met vriendelijke groet,
@@i = Arie Groeneveld
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
