import random as rd

leafduration = 4 # life time of a leaf
leafold =      2 # age at which a leaf is considered as old
maxorder =     4 # maximum number of branching order
radinc =    0.01 # increment of radius through time

maxduration = lambda order : int(5./(order+1))+5  # life time of an apex
branch_angle = lambda order : 8 # branching angle
# number of axe at a ramification
nb_axes = lambda order : rd.randint(2,4) if order > 2 else rd.randint(4-int((order+1)/2),5-int((order+1)/2))
up_angle = lambda t,order : -5        # up angle for lateral branches

# number total of iterations of the system
nbiter = sum([maxduration(o) for o in xrange(maxorder+1)])

module A # represent trunk apical meristem
module B # represent apical meristem of lateral branches
module L # whorl of leaf
module I # Internode


Axiom: _(0.05)@GcI(0.5,0.05)A(0,0)

derivation length: nbiter
production:
A(t,o) :
  if t < maxduration(o):
     # simply produces a metamer and ages the apex
     produce I(1,0.1)L(0,t)A(t+1,o)
  else:
      # produce a whorl of sympodial branches
      nbaxe = nb_axes(o)
      for i in xrange(nbaxe):
        nproduce [/(360*i/nbaxe)&(branch_angle(o))B(0,o+1)]


B(t,o) :
  if t < maxduration(o):
     # simply produces a metamer and ages the apex
     # reorient smoothly the branch toward the up
     produce ^(up_angle(t,o))I(1,0.1)L(0,t)B(t+1,o)
  else:
      # produce a whorl of sympodial branches
      nbaxe = nb_axes(o)
      for i in xrange(nbaxe):
        nproduce [/(360*i/nbaxe)&(branch_angle(o))B(0,o+1)]

L(t,n) :
  # ages the leaf. If too old, removes
  if t < leafduration :  produce L(t+1,n)
  else:   produce *

# Increment radius of internodes
I(s,r) --> I(s,r+radinc)
_(r) --> _(r+radinc)

homomorphism:
I(a,r) --> F(a,r)

L(t,p) :
    phi = 0 if p % 2 == 0 else 90  # phyllotactic angle
    col = 4 if t >= leafold else 2 # color is choosen according to age
    produce [/(phi)^(120);(col)~l(1)][/(phi)&(120);(col)~l(1)]

endlsystem