#Partial Answer

I think the answer may be

>! A

Reasoning:

>! If you look at each diagonal going from top left to bottom right, there appears to be a pattern of opposing ratios.

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>! Let $\rm B : W$ be the ratio of **B**lack shapes to **W**hite shapes, then the first diagonal (bottom left corner) is $1 : 3$. <br> <br> Next diagonal (left middle box and bottom middle box) is $4 : 0$ and $0 : 4$ respectively. <br> <br> Next diagonal (the middle diagonal with the missing box) have the ratios $1 : 3$ and $3 : 1$, so to me it makes sense that the missing box has a ratio of $1 : 3$.

That leaves either

>! A or F

Due to how the shapes in these boxes are positioned, I am leaning towards

>! A

However, my answer does no explain why the shapes are the way they are, but I think

>! It not only has to do with the ratio between colour, but also the ratio between edges. I noticed that when comparing boxes in the same diagonal, if a white circle (or donut) was in the same position as a black shape in another box, then that black shape is a diamond.

Hence, this answer is partial.