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Polar plots are generated by changing the current coordinate system to polar before issuing a plot command. The option set polar tells gnuplot to interpret input 2D coordinates as <angle>,<radius> rather than <x>,<y>. Many, but not all, of the 2D plotting styles work in polar mode. The figure shows a combination of plot styles lines and filledcurves. See set polar, set rrange, set size square, set theta, set ttics.
Polar heatmaps can be generated using plot style with surface together with set polar grid.
set size square set angle degrees set rtics set grid polar set palette cubehelix negative gamma 0.8 set polar grid gauss kdensity scale 35 set polar grid theta [0:190] plot DATA with surface, DATA with points pt 7