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I want to plot some phase diagrams that look professional (Example). I don't really know what tools are usually used to do this kind of diagrams, I've been looking around and found some alternative but I would like to know what is usually used by professional researchers to do this.

I have seen that there is a software tag but there is no usage guidance for that tag so I don't know if it would be on or off topic. Would a question like the above be on topic on this site? If not, where in the SE network could I ask it?

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I think this question is the most recent word on the matter, and that says software recommendation questions are off topic. I would group the question you're thinking about asking in the same category, and consider it off topic. It could also easily qualify as opinion-based.

You could bring your question up in our chat room, or it might be on topic at the Scientific Computation site.

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As always, this will boil down to the exact wording of the question on hand. If you just want to know how to plot the data like that, then no -- it won't be on topic. Valid answers are Excel, R, Matplotlib (python), Matlab, Mathmatica, Tecplot, gnuplot, and probably dozens more. Each is capable of generating a scatter plot/heatmap plot and that's all you are looking for there. All with varying amounts of effort and financial investment of course.

If you wanted to know how to use software may be used to analyze data and come up with whatever it is showing, the answer is a pretty solid maybe. But odds are good, for that image at least, the answer is going to just be "Get your data, read it into your plotting program of choice, generate image." Now, if you had the data and it was in some specialized file format that only astrophysicts would know how to use, that puts it back into the on-topic area here.

Places that it may appear on topic with different rules -- SciComp if you want help writing code to analyze data in some cool way or Cross Validated if you want help with reducing dimensionality/understanding statistical descriptions of data and visualizing the results.

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    $\begingroup$ On the softer side Academia is a venue to consider, but the OP should check first before posting there. $\endgroup$ – Emilio Pisanty Mar 1 '16 at 12:33

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