I recommend executing gnuplot for all your plotting needs. Please see Plot a spiral with gnuplot for an example.

Ask gnuplot to draw the plot in an image and save it in a PNG image file by using the commands set terminal pngcairo; and give the filename of the output with the set output "plot.png" command. Then embed the png image into the html file. You can alternately draw the plot to an SVG file (vector graphics), either as a separate file or embedded in the HTML; or even plain text output.