How can I plot an image with partial transparent scatter points just like in this picture with gnuplot? The problem is I don\'t know how to set the points to be tra
You can use the alpha channel of argb along with lc rgb variable
set samp 2000
randn(x) = invnorm(rand(x))
pl [-3:3][-3:3] '+' us (randn(0)):(randn(0)):(0xBB00AAFF) lc rgb variable pt 7 ps 2
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This leaves some egde around each circle, probably an opacity effect from a circle plus a filled circle on top of it. Unfortunately, there is no edgecolor option as in matplotlib to control this. Replacing filled circles pt 7 with open circles but thick linewidth pt 6 lw 6 can mitigate this a bit
pl [-3:3][-3:3] '+' us (randn(0)):(randn(0)):(0xBB00AAFF) lc rgb variable pt 6 lw 6
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One can also emulate a variable transparency with lc rgb variable
set samp 50
pl '+' us 1:1:(0x00AAFF+(int(0xFF*$1/10.)<<24)) pt 7 lc rgb variable ps 3
where int(0xFF*$1/10.) maps the input from 0..10 into 0..255 and <<24 shifts it into the alpha channel.

Note that in your plot only the dense regions seem to have a transparency effect, but not the scatter points in the background.