Is there a way to tell if data points are independent by looking at a the graph?

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Scatter plot

Say I have a scatterplot like the one above. Is there an easy way to determine whether or not the x and y values are independent from one another just by looking at the way the plots are placed on the graph? Or would I have to do mathematical computation to determine that? I can see that they are uncorrelated because there is no linear relationship between x and y but I dont know about independence...