gnuplot : plot function using palette/gradient linecolor : seems uniform, not gradient

Question

What does gnuplot need to plot the line of a function** using the palette linecolor i.e. as a gradient? (I tried terminal wxt 0 enhanced and svg, but will try more)? The documentation says palette is "used to color pm3d surfaces, heat maps, and other plot elements."

**POST-ANSWER NOTE No. 1: the function type will matter significantly - e.g. set parametric is quite different from, e.g, sin(x) - vide infra.

A number of Stack Overflow posts show how to use gnuplot to plot data points from an input data file as a gradient, using palette as the linecolor - these work as described in my hands and in the wxt and svg terminals (not shown - I will try some other ones).

I tried plotting sin(x) as described :

reset
unset key
set palette defined ( 0 "blue", 1 "red" )
plot sin(x) lw 3 lc palette z

I can see the gradient bar/key on the right, going from -10 to 10 (red), but the line appears to be at zero on the scale (in this case) - neither -10 (blue) or 10 (red) (see image):

as an aside : I thought set key off should keep the key from appearing on the plot? seems not (this apparently uses the default palette): (spoiler: to turn off the color scale/key bar on the right: unset colorbox - see comment that follows answer below.)

reset
set key off
plot sin(x) lw 3 lc palette z

An example of what I am looking for - a function plotted using a line that continuously changes color as displayed on the graph - is found in this SO post about matlab.

To conclude : is something missing from the gnuplot commands above to get a function like sin(x) plotted with a gradient - or perhaps recurring gradient, so it starts over again?

programs/environment used:

gnuplot 5.4 patchlevel 2

Ubuntu 22.04

POST-ANSWER NOTE No. 2: It is important to take care with the plot commands. If w l is omitted, as in this script:

### plot with lines with palette
### directly from the answer except omitting w l
reset session
unset key
set palette defined ( 0 "blue", 1 "red" )

# plot command to show plus signs:
plot '+' u 1:(sin(x)):(sin(x)) lc palette z
#
# original answer plot commands:
#plot '+' u 1:(sin(x)):(sin(x)) w l lw 3 lc palette z
### end of script

... literal plus signs + will be plotted :

Just worth being aware of it, is all.

Answer 1

If you want to use palette z for variable line color you have to give a z-column, e.g. plot ... (x):(y):(z).... This doesn't work directly if you are using functions.

But you have the special filename + (check help special-filenames) which is similar but where you can give columns, e.g.

plot '+' u 1:(sin($1)):(sin($1)) w lines palette z

Instead of $1 you could also use x.

Script:

### plot with lines with palette
reset session
unset key
set palette defined ( 0 "blue", 1 "red" )

plot '+' u 1:(sin(x)):(sin(x)) w l lw 3 lc palette z
### end of script

Result: