Self Organizing Maps (SOM) algorithm?

Question

Artificial intelligence

The SOM algorithm described here did not let me fully understand what exactly should be stored in the x and m vectors. For example, if you use this algorithm to approximate the simplest trigonometric function (sine or cosine), the coordinates of the function will be stored in the nodes of the map (is this true?), And the initial data (coordinates of several points) will be stored in the x vector?
Why do the nodes have to be exactly in a certain rectangular table, but cannot be in the same row (as it would be more logical in this case)? In general, it would be great to find a detailed description of the algorithm in Russian, because so far it raises more questions.