# set terminal png transparent nocrop enhanced font arial 8 size 420,320 # set output 'bivariat.5.png' set key inside right bottom vertical Right noreverse enhanced autotitles nobox set samples 4, 4 set isosamples 4, 4 set title "Plot of the ackermann function" set xrange [ 0.00000 : 3.00000 ] noreverse nowriteback set yrange [ 0.00000 : 3.00000 ] noreverse nowriteback integral_f(x) = (x>0)?int1a(x,x/ceil(x/delta)):-int1b(x,-x/ceil(-x/delta)) int1a(x,d) = (x<=d*.1) ? 0 : (int1a(x-d,d)+(f(x-d)+4*f(x-d*.5)+f(x))*d/6.) int1b(x,d) = (x>=-d*.1) ? 0 : (int1b(x+d,d)+(f(x+d)+4*f(x+d*.5)+f(x))*d/6.) f(x)=sin(x-1)-.75*sin(2*x-1)+(x**2)/8-5 integral2_f(x,y) = (xy-d*.5) ? 0 : (int2(x+d,y,d) + (f(x)+4*f(x+d*.5)+f(x+d))*d/6.) 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)