For very basic animations in Gnuplot you would need to set up a loop, decide what commands to give to Gnuplot and use the pipe utility to pipe that command into Gnuplot.

Example 1:

$ for ((i=-70; i<70; i++)); do echo -e "set sample 50000; set yrange [-40:40]; plot $i*sin(x)*cos(x) \n"; done | gnuplot

Example 2:

$ for ((i=-100; i<100; i++)); do echo -e "set isosample 100; spl [:] [:] [-100:100] $i*(sin(sqrt(x**2+y**2))/sqrt(x**2+y**2)) \n"; done | gnuplot -persist