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Topic: 8x8 bit patterns
Replies: 3   Last Post: Mar 13, 2013 12:09 PM

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Martin Brown

Posts: 250
Registered: 12/13/04
Re: 8x8 bit patterns
Posted: Mar 13, 2013 12:09 PM
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On 01/03/2013 15:35, Martin Brown wrote:
> On 01/03/2013 13:57, bert wrote:
>> On Thursday, February 28, 2013 10:51:02 AM UTC+1, Martin Brown wrote:
>>> I have a little puzzle where I think the answer is that it is not
>>> possible but having tried all the tricks I can think of cannot prove it.
>>>
>>> The problem arises from considering the possible bit patterns in an 8x8
>>> JPEG encoding square and searching for one that includes all possible
>>> states for subsampling up to 2x2 - that is 2x1, 4x1, 2x2
>>>
>>> It is obvious that the 4x1 subsampling requirement means that the final
>>> solution if it exists must be a permutation of the nibbles 0,1,...,15

>>
>> No, I think that's quite unlikely to be true, on the basis that there are
>> one or two 16-bit strings which, cyclically, contain all sixteen nibbles
>> (I remember using them as read/write patterns in disk tests). One 8-bit
>> row of your square can contain five different nibbles, not just two.

>
> Yes. But in the context of JPEG encoding the 8x8 grid is split into only
> the aligned 4x1 and 2x2 panels that will tile the plane.
>
> I did find a bug and now have a partial solution that gets 14/16 states.
> A complete solution still eludes me as does a proof it is impossible...


A much improved algorithm after a bit more thought gave a full solution:

0000 1110 0x0E
0001 0100 0x14
0010 1101 0x2D
1010 1000 0xA8

1011 0011 0xB3
1111 1100 0xFC
0101 1001 0x59
0111 0110 0x76

Read as aligned 4x1, 2x2 or 1x4 blocks every state is represented.

--
Regards,
Martin Brown



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