# set terminal png transparent nocrop enhanced font arial 8 size 420,320 
# set output 'bivariat.5.png'
set samples 4, 4
set isosamples 4, 4
set title "Plot of the ackermann function" 0.000000,0.000000  font ""
set xrange [ 0.00000 : 3.00000 ] noreverse nowriteback
set yrange [ 0.00000 : 3.00000 ] noreverse nowriteback
f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5
integral_f(x) = (x>0)?integral1a(x):-integral1b(x)
integral1a(x) = (x<=0)?0:(integral1a(x-delta)+delta*f(x))
integral1b(x) = (x>=0)?0:(integral1b(x+delta)+delta*f(x))
integral2_f(x,y) = (x<y)?integral2(x,y):-integral2(y,x)
integral2(x,y) = (x>y)?0:(integral2(x+delta,y)+delta*f(x))
ack(m,n) = (m == 0) ? n + 1 : (n == 0) ? ack(m-1,1) : ack(m-1,ack(m,n-1))
delta = 0.2
splot ack(x, y)