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Polyminoes
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You are currently reading a thread in /wsr/ - Worksafe Requests

Thread replies: 9
Thread images: 2
File: polymino problem.png (16 KB, 735x648) Image search: [iqdb] [SauceNao] [Google]
polymino problem.png
16 KB, 735x648
I must generate the smallest polymino, which when copied, can not overlay a rectangle of infinite size.
The smallest I've generated so far is 19-mino.
My hypothesis is that it's bigger than a 12-mino and smaller than a 19-mino.

Pic related:
Top = 20-mino, which meets the requirements. To the right of it - the placement of it's copies in order to achieve max coverable surface (10).
Middle = 16-mino, which does not meet the requirements. Copying it, a rectangle of infinite area can be achieved.
Bottom = 19-mino, which is the smallest I've found that meets the requirements.

help
>>
>>48102
Why can't you have
xx
x_x
xxx
>>
File: 7-mino copied.png (2 KB, 503x131) Image search: [iqdb] [SauceNao] [Google]
7-mino copied.png
2 KB, 503x131
>>48104
Can make an infinite rectangle.
I've theoretically checked all 2-mino to 12-mino and it doesn't seem possible, that the smallest can be <12-mino
>>
>>48109
Ah, a rectangle of infinite area, not infinite dimension.

This sounds like a job for computational AI, and maybe EC2.

Presuming it's not already a solved problem.
>>
>>48117
Hasn't been solved, hasn't been publicly discussed as far as I know. No research can be found.
>>
x_xxx_
x_x_xx
xxx___
>>
Anyway, this is more of a /sci/ problem.

Tesselations, etc.
>>
>>48109
What's your tessellation rule? Why not just shift it down one space while copying?
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>>48140
x_xxx_
x_x_xx
xxx___
x_xxx_
x_x_xx
xxx___
x_xxx_
x_x_xx
xxx___
x_xxx_
x_x_xx
xxx___

You forgot the Y axis.
Thread replies: 9
Thread images: 2
Thread DB ID: 489141



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