%!

/e 2.71828 def
/pi 3.141593 def
% z = [x y] -> e^z + z

/expn {
1 dict begin
aload pop
/y exch def
/x exch def
[ 
  e x exp y 180 mul pi div cos mul x add 
  e x exp y 180 mul pi div sin mul y add
] 
end
} def

% x y -> df/dx
/dfdy {
1 dict begin
aload pop
/y exch def
/x exch def
[ 
  e x exp y 180 mul pi div sin neg mul
  e x exp y 180 mul pi div cos mul 1 add
] 
end } def

/dfdx {
1 dict begin
aload pop
/y exch def
/x exch def
[ 
  e x exp y 180 mul pi div cos mul 1 add
  e x exp y 180 mul pi div sin mul
] 
end } def

% ------------------------------------------------------------

2.25 72 mul 5.5 72 mul translate

/S 36 def
S dup scale
1 S div setlinewidth

/k 3 def

/llx k neg def
/lly -1 def
/urx k def
/ury 1 def
% 20 x 10 grid
/N 10 def
/M N k mul def
/dx urx llx sub M div def
/dy ury lly sub N div def

% do vertical paths 
newpath
0 1 M { /i exch def
  % line at x = llx + dx*i
  /x llx dx i mul add def
  /y lly def
  [x y] expn aload pop 
  /fy exch def /fx exch def % P0
  fx fy moveto
  % calculate df/dy
  [x y] dfdy aload pop 
  dy mul /dfy exch def 
  dy mul /dfx exch def

  1 1 N { /j exch def
    fx dfx 3 div add fy dfy 3 div add % P1

    % calculate next (x, y)
    /y lly dy j mul add def
    % calculate next df/dy
    [x y] dfdy aload pop 
    dy mul /dfy exch def 
    dy mul /dfx exch def
    [ x y ] expn 
    aload pop
    /fy exch def /fx exch def

    fx dfx 3 div sub fy dfy 3 div sub % P2
    fx fy curveto % P3
  } for

} for
stroke

% do horizontal paths 
newpath
0 1 N { /j exch def
  % line at x = llx + dx*i
  /y lly dy j mul add def
  /x llx def
  [x y] expn aload pop 
  /fy exch def /fx exch def % P0
  fx fy moveto
  % calculate df/dx
  [x y] dfdx aload pop 
  dx mul /dfy exch def 
  dx mul /dfx exch def

  1 1 M { /i exch def
    fx dfx 3 div add fy dfy 3 div add % P1

    % calculate next (x, y)
    /x llx dx i mul add def
    % calculate next df/dy
    [x y] dfdx aload pop 
    dx mul /dfy exch def 
    dx mul /dfx exch def
    [ x y ] expn 
    aload pop
    /fy exch def /fx exch def

    fx dfx 3 div sub fy dfy 3 div sub % P2
    fx fy curveto % P3
  } for
} for
stroke