Tutorial „Modelling in the language XL“University of Göttingen (Germany), September 21/22, 2009

Winfried Kurth

Steps towards modelling poplar trees

related material: XL code files sm09_e??.rggURL http://www.uni-forst.gwdg.de/~wkurth/and drive T:\rgg on CIP pool stations

increasingly elaborated versions of a (preliminary) model of 1-year-old, unbranched poplar trees

versions:

sm09_e37.gsz modules with user-defined methods; use of transformation matrices

sm09_e38.gsz internode elongation, counting the days

sm09_e39.gsz collection of all constants at the head of the programme

sm09_e40.gsz introduction of three leaf maturity classes, arrays with growth parameters

necessary for the distribution of assimilates:

modelling of transport processes

approach: substrate flows from elements with high concentration to neighbour elements with low concentration (principle of diffusion)

example:

sm09_e41.rgg (concentration of substrates is here visualized by diameter)

module Internode(super.diameter) extends F(100, diameter);

protected void init() [ Axiom ==> P(14) Internode(1) P(2) Internode(1) P(4) Internode(1) P(15) Internode(60); ] public void transport() [ i_top:Internode < < i_bottom:Internode ::> { float r = 0.1 * (i_bottom[diameter] - i_top[diameter]); i_bottom[diameter] :-= r; i_top[diameter] :+= r; } ]

(two reverse successor edges, one after the other)

for light interception / photosynthesis:

a simple model of overshadowing

model approach (strongly simplifying): overshadowing of an object occurs when there are further objects in an imagined cone with its apex in the object, opened into z direction (to the sky).

example:

sm09_e42.rgg competition of three 2-dimensional model plants for light

module Segment(int t, int ord) extends F0;module TBud(int t) extends F(1, 1, 1);module LBud extends F(0.5, 0.5, 1);

Vector3d z = new Vector3d(0, 0, 1);

protected void init() [ Axiom ==> P(2) D(5) V(-0.15) [ TBud(-4) ] RU(90) M(600) RU(-90) [ TBud(0) ] RU(-90) M(1200) RU(90) [ TBud(-8) ]; ] public void run() [ TBud(t), (t < 0) ==> TBud(t+1); x:TBud(t), (t >= 0 && empty( (* s:Segment, (s in cone(x, z, 45)) *) ) ) ==> L(random(80, 120)) Segment(0, 0) [ MRel(random(0.5, 0.9)) RU(60) LBud ] [ MRel(random(0.5, 0.9)) RU(-60) LBud ] TBud(t+1); y:LBud, (empty( (* s:Segment, (s in cone(y, z, 45)) *) ) ) ==> L(random(60, 90) Segment(0, 1) RV0 LBud; Segment(t, o), (t < 8) ==> Segment(t+1, o); Segment(t, o), (t >= 8 && o == 1) ==>> ; /* removal of the whole branch */ ]

a further rule type in XL:

instantiation rules

purpose: replacement of single modules by more complicated structures, only for visual representation(similar as for interpretive rules)

• but: less data are stored (less usage of memory)

• in contrast to interpretive rules, no turtle commands with effect on other nodes can be used

further, arising possibility: „replicator nodes“ for copying and relocation of whole structures

instantiation rules: syntax

no new sort of rule arrow

specification of the instantiation rule directly in the declaration of the module which is to be replaced

module A ==> B C D;

replaces (instantializes) everywhere A by B C D

example

sm09_e43.rgg

const int multiply = EDGE_0; /* user-defined edge type */

module Tree ==> F(20, 1) [ M(-8) RU(45) F(6, 0.8) Sphere(1) ] [ M(-5) RU(-45) F(4, 0.6) Sphere(1) ] Sphere(2);

module Replicator ==> [ getFirst(multiply) ] Translate(10, 0, 0) [ getFirst(multiply) ];

public void run1()[Axiom ==> F(2, 6) P(10) Tree;]

public void run2() [Axiom ==> F(2, 6) P(10) Replicator -multiply-> Tree;]

inserts all what comes after the „multiply“ edge

Tree is instantiated with the red structure

further steps towards the poplar model

sm09_b44.gsz

sm09_b45.gsz

in poplar.gsz we have additionally:

- insertion of a rule block for the angles, change of angles during growth

- insertion of an object „Sun“ which changes its position relative to the plant during the day

Thank you for your attention!