nx(x,y,a,b) = y + 1 - a*x*x
ny(x,y,a,b) = b*x

unset key
set samp 50000
a = 1.4
b = 0.30
set xrange [-1.5:1.5]
set term pngcairo enh font ",10" size 480,360
set out "henon.png"
set title sprintf("Henon: a = %.3f, b = %.3f", a, b) font ",14" 
xp = yp = xc = yc = 1.0
plot '+' u (xc=nx(xp,yp,a,b), yc=ny(xp,yp,a,b), xc):\
            (xp=xc, yp=yc, yc) lc rgb "dark-green" w d