Visual Pattern Recognition Test

[asmani]

Dear moderator, if the thread is irrelevant to this forum section, please move it to the right section. Thanks.

 

[mfb]

You can find some pattern for all 128 possible options.

I found a nice pattern that predicts "all black", and a slightly less nice pattern that predicts "the bottom and the two right white, rest black". If you have a different answer, then you can try to find patterns for these answers.

Edit: With a small extension, I can also justify "the bottom one and the bottom right are white, the rest is black".

 

[asmani]

Could you please illustrate your answer?

 

[mfb]

What do you mean by "illustrate"? Make a picture of the answer? Is the description unclear?

Explain how I got it? That would take the fun out of it. But I'll give a hint: I treated the images in the last row as result of an operation on the two images above in each case.

 

[asmani]

I'm sorry, that was bad English. I meant "Make a picture of the answer".

Can you give a hint on what type of operation? I've tried unions, intersections, symmetric differences, shifts, reflections, rotations, reversing, and some combinations of these operations, none of them worked. should I search through more combinations of these operations? Or other operations than those? You must be a genius that you found the answer in less than 10 minutes. I keep telling myself I must think outside the box, but still no results. Shouldn't be so obsessed with my intelligence...

 

[asmani]

predicts "all black"

Oh, did you mean the answer to "?" is all black? Well, that doesn't need a picture.

 

[asmani]

I found this, but it's not very nice: Each element of the first row is some reflection of the union of the other two in its column. So here is the answer:

 

[mfb]

Oh, did you mean the answer to "?" is all black? Well, that doesn't need a picture.

Yes, and I was confused why you asked for a picture. I mean, sure, I could make one, but I didn't see the point.

I don't think I found "the" answer, and I don't even think there is "the" answer. There are many answers.
What I found: For every position, count the number of white dots at this position and at the surrounding positions in the first two rows. If the number is 5 or larger, make a white dot in the third row.

As an example, consider the top spot in the first column: We have the top, top left and center dot in the first row and the top dot in the second row, for a total of 4 white dots. Smaller than 5, so this spot is black.

This algorithm leads to "all black" in the bottom right.

The two columns we have only constrain what the dot color has to be for 2 to 6 and 8, but we don't have 1 anywhere. A slight modification from the rule above: If the number is 1, or 5 or larger, make the dot white. That leads to three white dots.

 

[asmani]

I understand what you mean by many answers.

That's a nice pattern, thanks!