using gnuplot to read in - not output - a png image, or many, in one session - as an "overlay" - gnuplot

Question

I want to read multiple png files - which themselves were created with gnuplot (terminal png) - in order to achieve an "overlay" - that is, a number of functions plotted together one on top of the other, with no background. This apparently could be done with gnuplot in one session.
I found this idea from the Linux Gazette article "Plotting the spirograph equations with 'gnuplot' ", from 2006 :
https://linuxgazette.net/133/luana.html
I am stuck on a number of error messages (vide infra) :
line 0: Bad data on line 1 of file [...]
line 0: warning: using default binary record/array structure
line 0: Too many using specs for this style
Looking for solutions, I read in the help pages ( http://gnuplot.info/docs_5.5/loc7742.html ) that gnuplot can read png images :
plot 'file.png' binary filetype=png
... and I have looked into using pngcairo instead of png itself. I am using eog to view the .png images. Here is sample code which generates the error above, and more if adjusted :
set size ratio -1
set nokey
set noxtics
set noytics
set noborder
set parametric
i2p = {0,1}*2*pi
set terminal png
t0 = 0
t1 = 1
#---------------------------------------------
# plot first function in the gnuplot session :
#---------------------------------------------
test01(t) = exp(i2p*(2*t))
set output "solve_png_problem_15nov22a.png"
plot [t=t0:t1] 1*real(test01(t)),1*imag(test01(t)) lc 1
#---------------------------------------------------
# plot second function in the same gnuplot session :
#---------------------------------------------------
test02(t) = + 3*1.0**20 * exp(i2p*(-3*t+20/200. )) + 3*1.0**19 * exp(i2p* (2*t+20/200.))
set output "solve_png_problem_15nov22b.png"
plot [t=t0:t1] 1*real(test02(t)),1*imag(test02(t)) lc 2
#------------------------------------------------------------
# last plotting to apparently "overlay" the two plots above :
#------------------------------------------------------------
set terminal png size 600,600
set output "solve_png_problem_15nov22_overlay.png"
set noparametric
plot "solve_png_problem_15nov22a.png", "solve_png_problem_15nov22b.png"
.... the reduced sample code is generated from the awk script supplement to the article - see it for detail :
https://linuxgazette.net/133/misc/luana/spirolang.awk.txt
The functions are nontrivial so they were kept in tact, as the associated settings might be causing the problem. The individual images look ok, so I think the problem is in the last plot command.
I read in the help pages that gnuplot can read png images :
plot 'file.png' binary filetype=png
... and also filetype=auto, and I have looked into using pngcairo instead of png itself, with no progress ; I have read the results of Google searches for the error messages. I have read the help pages on terminal, png, image, binary, and so on. I was expecting gnuplot to simply recognize the file was a png image that gnuplot itself generated, using the png terminal. What actually results is the error"Too many using specs for this style". For this, I have tried moving the position of the "binary filetype=png" in the code, which give the error "line 0: Bad data on line 1 of file [...]". I have also tried using programs outside gnuplot, such as montage and composite (ImageMagick).
gnuplot version 5.4 patchlevel 2
Ubuntu 22.04
post-answer update:
TL;DR : use svg terminal.
I saved a lot of grief by simply using the svg terminal. The original work must have been published before gnuplot got the svg terminal. I still need to work svg into the original script - but svg will make it a lot easier.

Answer 1

Try this in GNUPLOT.
gnuplot<<EOF
set terminal png medium size 600,600 background rgb "white"
set size ratio -1
set nokey
set noxtics
set noytics
set noborder
set parametric
i2p = {0,1}*2*pi
t0 = 0
t1 = 1
#---------------------------------------------
# plot first function in the gnuplot session :
#---------------------------------------------
test01(t) = exp(i2p*(2*t))
set output "solve_png_problem_15nov22a.png"
plot [t=t0:t1] 1*real(test01(t)),1*imag(test01(t)) lc 1
#---------------------------------------------------
# plot second function in the same gnuplot session :
#---------------------------------------------------
test02(t) = + 3*1.0**20 * exp(i2p*(-3*t+20/200. )) + 3*1.0**19 * exp(i2p* (2*t+20/200.))
set output "solve_png_problem_15nov22b.png"
plot [t=t0:t1] 1*real(test02(t)),1*imag(test02(t)) lc 2
#------------------------------------------------------------
# last plotting to "overlay" the two plots above :
#------------------------------------------------------------
set output "solve_png_problem_15nov22_overlay.png"
plot \
[t=t0:t1] 1*real(test01(t)),1*imag(test01(t)) lc 1, \
[t=t0:t1] 1*real(test02(t)),1*imag(test02(t)) lc 2
EOF
First Result:
Second Result:
Combined Result: