Polyminoes
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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
>>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?
>>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.