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# The Leuwenberg model

The original Hallé sketch and the resulting 3D Lpy model:

The following script generates an architecture:

```import random as rd

leafduration = 3 # life time of a leaf
leafold =      2 # age at which a leaf is considered as old
maxorder =     4 # maximum number of branching order

maxduration = lambda order : int(10./(order+1))+3  # life time of an apex
branch_angle = lambda order : 60+30*((maxorder-order)/maxorder) # branching angle
nb_axes = lambda order : rd.randint(3,5)  # number of axe at a ramification
up_angle = lambda t,order : 7        # 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: _(0.1)@GcI(0.5,0.1)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)]
produce T

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)]
produce T

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

homomorphism:

I(a,r) --> F(a,r)
T --> @Ge_(0.05);(3)F(0.5)@O(0.2)

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

endlsystem``` 