set terminal eps color
set output "brachistochrone.eps"
set nokey
set noborder
set noxtics
set noytics
set size ratio -1
set parametric
plot [t=0:5] t-sin(t), cos(t)-1 with lines lw 5
Then touched up with inkscape and exported as png. (Creating png output from gnuplot is bad since then the curve won't be properly anti-aliased.)
This image was copied from wikipedia:en. The original description was: The cycloid as brachistochrone. Cycloid created with gnuplot using the commands set terminal eps color set output "brachistochrone.eps" set nokey set noborder