gnuplot and "extra" graphics objects (like a dot or circle) in any general location on plot (e.g. in the "title" area) - graphics

Question

Consider the following example script :
reset session
set multiplot layout 1,2
set title "."
plot sin(x)
set title "."
plot sin(x**2)
unset multiplot
... one can see that the set title "." is a kludge for, ideally, a nicer dot - perhaps what is called a "bulletpoint". While I could pursue this kludge, using O, or other font sizes, point sizes, or {/Symbol } (in progress), or terminals of the LaTeX variety (because there are pretty good mathematical symbols I could use like cdot), it would be interesting to know in general - a simple shape like a dot or square, imposed somewhere on the plot, but outside the usual set title or label which have certain rules with the fonts and such.

Answer 1

It's still not fully clear to me what you want to achieve. Placing a point which tunable size as title or at the place where the title usually would be?
You can use set label with option point (check help label). You can set different point types, type test in the gnuplot console to see the available pointtypes. It's not clear, why you wrote that you don't want to use labels. Maybe with the example below we'll get a step further.
Script:
### place a point somewhere on the canvas
reset session
set multiplot layout 1,2
set title "."
plot sin(x)
set title " "
set label 1 at graph 0.2,1.05 point pt 7 ps 0.25 lc "dark-violet"
set label 2 at graph 0.3,1.05 point pt 7 ps 0.50 lc "blue"
set label 3 at graph 0.4,1.05 point pt 7 ps 0.75 lc "cyan"
set label 4 at graph 0.5,1.05 point pt 7 ps 1.00 lc "green"
set label 5 at graph 0.6,1.05 point pt 7 ps 1.25 lc "yellow"
set label 6 at graph 0.7,1.05 point pt 7 ps 1.50 lc "orange"
set label 7 at graph 0.8,1.05 point pt 7 ps 1.75 lc "red"
plot sin(x**2)
unset multiplot
### end of script
Result:

Answer 2

You can place a graphical object (drawn with vectors and/or solid fill) using the command set object {circle|rectangle|polygon} at .... See User Manual or interactive help for details.
You can use any unicode character including math symbols and even emojis in a title or label. Yes, you must have a font available that contains that character, but these days that is not much of a limitation. For example:
set title "Various solar symbols: ☀☼🌣☉"
Even if you have trouble entering the desired symbol via keyboard or cut-and-paste, current gnuplot allows you to specify the unicode symbol as an escape sequence:
set label 1 "Solar symbol" at graph 0.5, 1.0 point pointtype "\U+2609"
set border 3; unset tics
plot 1/exp(x) notitle

Answer 3

I gathered these approaches in a demonstration script the sin(x) functions are just for show :
reset session
unset key
#
set grid x,y
set style fill solid 1.0
set multiplot layout 2,2
#
set title "."
plot 1*sin(x)
unset title
#
set title "O"
plot 2*sin(x)
unset title
unset object
#
# series of objects
# only valid on on the specific plot area
# not outside the e.g. axes or border
set object circle at 1,1
set object circle at 1,2
set object circle at 1,3
plot 3*sin(x)
unset object
#
set label 1 at graph -0.1,1.10 point pt 7 ps 1.00 lc "black"
set label 2 at graph 0.0,1.10 point pt 7 ps 1.00 lc "black"
set label 3 at graph 0.5,1.05 point pt 7 ps 1.00 lc "black"
set label 4 at graph 0.5,1.10 point pt 7 ps 1.00 lc "black"
plot 4*sin(x)
unset label
#
unset multiplot
unset output
I couldn't get fill style solid 1.0 to work on set object circle the way I wanted so I left it, perhaps there is a way. One can see the circle gets cut off on the edge. The label coordinates also have requirements (see manual).
To be clear, I am writing this "answer" but the question is only "answered" because of theozh and Ethan (thanks!).