#Proj3.txt: Maple package for Project 3 of Math 336 (Rutgers Univ., Fall 2025 taught by Dr. Z. (aka Professor Doron Zeilberger))
read `DMB.txt`:


print(`This is Proj3.txt, a Maple package accompanying Project 3 of Dr. Z.'s Math 336 (Dynamical Models in Biology), Fall 2025`):
print(` Project Leader: Aurelia Altzman `):
print(``):
print(`Other members : `):
print(` Adriana Ferreira, Palash Keswani `):
print(`For a list of the procedures done by this team type: HelpX(); For Help with a specific procedure, type: Help3(ProcedureName);`):

with(plots):

Help3:=proc()
  if nargs=0 then
    print(`The available procedures are:  `):
  elif nargs=1 and args[1]=PROC then
    print(``):
  elif args[1] = detectPeriod then 
    print(`guesses the period of an orbit. Chaotic orbits should be at least 17 elements long`)
  elif args[1] = F    then print(`An example logistic equation. F(n) = n * x * (1-x)`):
  elif args[1] = OrbF then print(`Returns an Orbit of F(n) of length 17 w/ initial value 0.2`):
  else
    print(`There is no Help for`, args):
  end:

end:
detectPeriod := proc(L) 
  if L[1] = L[2] then return 1 
  elif L[1] = L[3] then return 2
  elif L[1] = L[4] then return 3 
  elif L[1] = L[5] then return 4 
  elif L[1] = L[9] then return 8 
  elif L[1] = L[17] then return 16 
  else return 16 
  end:
end:
F := proc(n) return n*x*(1-x) end:
OrbF := proc(n) Orb(F(n), x, 0.2, 1000, 1016) end:
take := proc(L) L[1..detectPeriod(L)] end:
showBiforcations := proc() 
  Digits := 20:
  local L := []:
  local i:
  for i from 25 to 200 do 
    local n := 2 + 0.01 * i;
    local elem:
    for elem in take(OrbF(n)) do 
      L:= [op(L), [n, elem]]:
    end:
  end:
  pointplot(L);
  #return L 
end: