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I'm trying to make a simulation for Chladni plates

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the diagram above shows the patterns on rectangular plates, and relates them to 2 values (n, m) many of the explanations suggest that (n) is the number of lines parallel to the diagonals, and (m) is the number of perpendicular lines, which does not seem to be true in many cases, like the third pattern of the third line, no lines parallel to the diagonals although (n = 2) I can't relate those explanations to this Diagram, my question is what are (n) and (m) exactly? do they represent any property of the patterns?

Ali HS
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The lines in the pictures show the nodes of the various modes, that is, the location of the points that do not move, while the rest of the points move up and down at the frequency $f_{nm}$ of the related mode. In a rectangular plate, those frequencies take the form $\alpha\left(\frac{n^2}{a^2} + \frac{m^2}{b^2}\right)$ see this article, hence the labels.