LC = "'white'" 
set term pngcairo size 480,360 backgr "#003366" font ",10"
set samples 200
set tics tc @LC
set border lc @LC
set key tc @LC

D = 10
do for [i = 2:50] {
  t = i * 0.005
  set out sprintf("img%03d.png",i)
  plot [-10:10] [0:1] exp(-x**2/(4*D*t))/(2*sqrt(pi*D*t)) lw 2 lc @LC
}

system("convert -adjoin -delay 10 img*.png diffusion1.gif")
system("rm img*.png")