How to make points one color when a third column equals zero, and another color otherwise, in Gnuplot?

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This is probably close to what you want:

set palette model RGB defined ( 0 'red', 1 'green' )
plot[0:5][0:6] "file.dat" u 1:2:( $3 == 0 ? 0 : 1 ) with points palette

You could go one step further and remove the “noise”:

unset key
unset colorbox
plot[0:5][0:6] "file.dat" u 1:2:( $3 == 0 ? 0 : 1 ) with points pt 7 ps 3 palette

if only the differentiation between zero and non-zero matters.

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