Lindenmayer systems

3D tree branching model

Fri, 09/03/2012 - 11:26 — jonathanm

ModelId:

branching1

SimileVersion:

5.9

This is a demonstration of Simile’s ability to handle fractal models.

L-system (Lindenmayer system) models are based on the idea that a complex structure can be obtained by repeatedly applying quite simple rules to a simple initial stucture. Thus, for example, the branching structure of a mature tree can be arrived at by applying simple rules to a seedling: rules such as "replace a bud by an extension to the branch, a side shoot, and two buds".

Equations:

Equations in ../Desktop

variable: age=time(1)-init_time(1)
variable: nbranch=sum({one}) where [{one}=internode/one]
variable: nterminal=sum({terminal}) where [{terminal}=internode/terminal]
variable: volume=sum({volume}) where [{volume}=internode/volume]

Equations in internode

variable: x1=d*sin(a1/57.3) where [a1=a1,d=d]
variable: y=element([coords],2)+d*cos(a1/57.3) where [[coords]=coords,d=d,a1=a1]
variable: x=element([coords],1)+x1*cos(a2/57.3) where [[coords]=coords,a2=a2,x1=x1]
variable: old coords=last([shift_coords]) where [[shift_coords]=shift coords]
variable: one=1
variable: in coords=[coords_0] where [{[coords]}=../connected/coords (to internode in Parent),[coords_0]=../connected/coords (to internode in child)]
variable: coords=(if index(1)== -1 then [0,0,0,0,0] else [in_coords]) where [[in_coords]=in coords]
if index(1)== -1 then [0,0,0,2] else [in_coords]
variable: nabove=sum({one}) where [{one}=../connected/one (to internode in Parent),one_0=../connected/one (to internode in child)]
variable: terminal=(if nabove==0 then 1 else 0) where [nabove=nabove]
variable: shift coords=[x,y,z,a1,a2] where [x=x,y=y,z=z,a1=a1,a2=a2]
variable: z=element([coords],3)+x1*sin(a2/57.3) where [[coords]=coords,a2=a2,x1=x1]
variable: a1=element([coords],4) where [[coords]=coords]
variable: a2=element([coords],5) where [[coords]=coords]
compartment: size=0.4
flow: growth=0.2
variable: d=rand_const(1.5,2)
variable: display=[element([coords],1),element([coords],2),element([coords],3),x,y,z] where [[coords]=coords,x=x,y=y,z=z]
variable: volume=d*3.14157*(size/2)^2 where [size=size,d=d]
creation: cr1=1
reproduction: rep1=(if terminal==1 then 2 else 0) where [terminal=terminal]
if terminal==1 and rand_var(0,1)<20/nterminal then 2 else 0
variable: MyParent=parent(1)
variable: Me=index(1)

Equations in connected

variable: coords=[old_coords]+[0,0,0,a1_change,a2_change] where [[old_coords]=../internode/old coords (from internode in Parent),[old_coords_0]=../internode/old coords (from internode in child),a1_change=a1 change,a2_change=a2 change]
variable: one=one_0 where [one=../internode/one (from internode in Parent),one_0=../internode/one (from internode in child)]
variable: a1 change=rand_const(-25,25)
variable: a2 change=rand_const(-40,40)

Results:

L-systems architechture