#--------------------------------------------------------------------------
# Animation of the string instanton solutions. This program generates a   |
# .dat numeric data file for each frame of the animation sequence.        |
# Usage (on UNIX): maple StringTheory.data.txt &                          |
#                                                                         |
# Bob Bacus c.1997                                                        |
#------------------------- User input parameters --------------------------
p:=2:                 # F=e^(Pi*p*z)                                      |
q:=2:                 # G=e^(Pi*q*z)                                      |
startframe:=0:        # Frame to start from                               |
endframe:=400:        # Frame to end on                                   |
points:=400:          # Number of data points per frame                   |
lmin:=-1:lmax:=1:     # Range for the time parameter                      |
smin:=-1:smax:=1:     # Range for the length parameter                    |
# ---------------------------- Main Program -------------------------------
gc(300000):interface(screenwidth=200):Digits:=4:
readlib(unassign):readlib(write):
unassign('t'):unassign('l'):unassign('n'):unassign('u'):unassign('s'):
assume(t,real):assume(s,real):
z:=t+I*s:
#------------------------ X=[Im(F),Re(F),Re(G),Im(G)] --------------------------
# Torus Knots: F=z^p, G=-z^q
imf:=Im(expand(z^p)):
ref:=Re(expand(z^p)):
reg:=Re(expand(-z^q)):
img:=l:
# Closed String Type V: F=e^(Pi*p*z), G=e^(Pi*q*z)
imf:=((l/sin(Pi*q*s))^(p/q))*sin(Pi*p*s):
ref:=((l/sin(Pi*q*s))^(p/q))*cos(Pi*p*s):
reg:=(l/sin(Pi*q*s))*cos(Pi*q*s):
img:=l:
# Closed string Type B: F=e^(Pi*p*z), G=e^(Pi*q*z)
imf:=sinh(Pi*p*arcsinh(l/(cos(Pi*q*s)-sin(Pi*q*s))))*(cos(Pi*p*s)+sin(Pi*p*s)):
ref:=cosh(Pi*p*arcsinh(l/(cos(Pi*q*s)-sin(Pi*q*s))))*(cos(Pi*p*s)-sin(Pi*p*s)):
reg:=-cosh(Pi*p*arcsinh(l/(cos(Pi*q*s)-sin(Pi*q*s))))*(cos(Pi*p*s)+sin(Pi*p*s)):
img:=l:
#-------------------------------------------------------------------------------
l:=(lmax-lmin)/(endframe-startframe)*n+lmin: # n represents frame number; l is the proper time
v:=(smax-smin)/(points-1):
for n from startframe by 1 to endframe do
  open(cat(convert(p,string),`x`,convert(q,string),`-`,convert(n,string),`.dat`)):
  writeln(evalf(l)):
  writeln(points):
    for u from smin by v to smax do
      writeln(evalf(subs(s=u,[imf,ref,reg]))):
    od;
  close():
od;
unassign('t'):unassign('l'):unassign('n'):unassign('u'):
#--------------------------------------------------------------------------
# Use `StringTheory.data2gif.txt` to generate .gif frames.                 |
#-------------------------------------------------------------------------- 
close():
quit: