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12. Aug. 2007

Introduction  /  File Syntax Notation  /  Download  /  Examples  /  Stochastic L-Systems  /  Notation  /  Other Applications  /  Links  /  Books

Introduction
The Lindenmayer System language also known as L-Systems was defined by Aristid Lindenmayer
in the book 'The Algorithmic Beauty of Plants, Springer Verlag'.
Text on the back cover:
"This book is for * Computer graphics professionals * Biologists, * Theoretical computer scientists and mathematicians who will discover that the mathematical beautiful theory of L-Systems has important practical applications * Individuals interested in fractals, L-Systems and Artifical Life".


 Aristid Lindenmayer 
Aristid Lindenmayer (1925-1989)



LSystem File Syntax Notation:
To load and save such definitions from a text file, I use a notation which is an extention to the Virtual Reality Modeling Language (see Extensibility of VRML 1.0 Specification or VRML 1.0c Specification).
You can see the syntax extension on the right side.
After the property name definition included by '[...]'  the default values are defined.

name
should have no blancs included.
info is an optional information text  limited to 80 characters.
link is an optional hone page reference.
angle defines how many degrees the 3d turtle should turn.
step defines the step length you go on commands like F, f, G or g.
segments defines the number of cylinder planes which will be draw instead of lines, if the thickness is greater than 1.0.
thickness defines the diameter of the cylinder for one turtle step.
factor defines a multiplication value per deep step for resizing the whole drawing figure.
deep defines the number of recursions until the replacement of the rule characters stops.
colors defines an optional color array that defines the color palette to use.
The axiom defines the starting rule for the LSystem interpreter.
The rules defines the replacement statements.
LSystem Definition Syntax and default values:
LSystem 
{ fields
[ SFString name, SFString info,
SFString link,
 SFFloat angle, SFLong segments,
SFFloat step, SFFloat thickness,
SFFloat factor,
SFLong deep, MFColor colors,
SFString axiom, MFString rules
]
name "unknown" info ""
link ""
angle 30 segments 6
step 100.0 thickness 1.0
factor 0.8
deep 4 colors [ ]
axiom A
rules [A=AF+]
}


Download:
Download LinSy3d.zip 
LinSy3d.exe

If you want to create your own Lindenmayer Systems figures or if you only want  to play around with the predefined LSystem definitions than download my new
Lindenmayer System Interpreter
 LinSy3d.exe   v1.03
this is new

The visualization uses the 3d-Engine FliSp3d. Therefore many parameters can be changed interactivly, e.g. the background picture or the transparency of lines, planes and sprites.
Get more information about FliSp at this link.

Note:
Now you can save a lindenmayer system as text file and you can load LSystem files which may contain a collection of many LSystem definitions.
Statements '(' and ')' for defining values are still not implemented at the moment.
Sorry - but ... I am working on this features.
LSystem Selection Dialog LSystem selection
To select a predefined LSystem figur press right mouse button on main screen and choose a figure with the menu command  'Select figure / ...'.

Loading and Saving LSystem collection files
On Tab Select you can load and save LSystem text files, which can have one or more LSystem definitions pressing Load File... or Save File ... button.
Displayed files can be loaded again easily by pressing button  Load Again  e.g. after corrections of the LSystem file done with a text editor.
If you want to load all LSystem file of a directory press Load All (v1.04).
After selecting a LSystem item of a predefined or a loaded  LSystem collection, you can view it by pressing button View or with a double click to it. Pressing button Edit will copy all parameters to the edit fields and change to tab Edit for further changes.
LSystem Editing Dialog How to edit LSystems with LinSy3d
The dialog for editing LSystems will be automatically opened at program start.
You can open this dialog also by the menu command 'Edit / Lindenmayer Systems... Ctrl-F8'
Select Tab Edit and press button Get to get all parameters of the actual displayed LSystem.
If you want see the effect of changed parameters, press the Set button.
If you want to see changes immediately, turn on link drawing.
You can easily copy the whole parameters to e.g. a text file with the Lindenmayer text file (*.lsy) syntax  if you press the Copy button and paste the copied text there.
The Save... button will start the file saving dialog to save the LSystem as a *.lsy text file with a single LSystem definition.

Examples:
The following table show you only some few examples.  Many examples are predefined within the LinSys3d application.
But most of the LSystem definitions are defined in the included Lindenmayer definition files.
p120a.gif
LSystem
{ name "GrowingLeaf2Bush-120"
info "bush of branches with growing leafs"
angle 22.5
factor 0.74
deep 8
axiom A
rules
[ "A=///BY///BYA"
"B=[&Y[+L][-L]YBF]"
"L=FF'{+X.-X.-X.+|+X.-X.}"
"X=gX"
"Y=FY"
]}
p123a.gif
LSystem 
{ name "cordate leaf plant 123"
info "plant with cordate leafs of page 123"
angle 6.0
factor 0.8
deep 14
axiom "R9'~S"
rules
[ "R:?LLLFR"
"L:!15/[EA]"
"E:&E"
"A:'F[B][C]"
"B:/[++B{.].D.}"
"C:\[--C{.].D.}"
"D:gD"
"X:FX" ]
}
facette leaf bush
LSystem
{ name "LeafPlant1-124"
angle 11
thickness 4
factor 0.8
deep 9
axiom "R4'~S"
rules
[ "R=LLLL!R"
"L=/////['&&&&&[A]B]F"
"A={[+++++Y.]&Y[+++++X.].}A"
"B={[-----Y.]&Y[-----X.].}B"
"X=Y"
"Y=gY"
]}
p124c.gif
LSystem
{ name "LeafPlant2-124"
angle 6
factor 0.83
deep 8
axiom "I"
rules
[ "I=/////LLLLL'FFFI"
"L=////////////[&&&&&'FF[A]B]"
"A={[+++++Y.]&&Y[+++++X.].}A"
"B={[-----Y.]&&Y[-----X.].}B"
"X=Y"
"Y=gY"
]}
p121a.gif
LSystem
{ name "BlueBerryBush1"
info "Blue berry bush 1, 2003 Gerd Platl"
link "http://www.geocities.com/gplatl/LSystem/LSystem.html"
angle 11.25
factor 0.74
deep 10
axiom "9a"
rules
[ "a=4/[^^l]"
"l=[X^[++B]r]"
"r=4X^[--B]l"
"B=[b[3+L][3-L]XB]"
"L=F'{+Y.-Y.-Y.+|+Y.-Y.}"
"X=FX"
"Y=gY"
"z=4/[^B]"
"b=X8'[^^4F~S]8`"
]}
palm1a.gif
LSystem
{ name "Palm1"
angle 2
factor 0.88
deep 8
axiom "a'12b"
rules
[ "a=a&~xf"
"b=15\[16&cA]"
"c=c2&"
"A=F[12+B]8&[A][12-B]"
"B=F8&B"
]}

pine3d.gif
LSystem
{ name "Pine3d" info "Pine schematic in 3d"
angle 5 thickness 3
factor 0.8 deep 8
axiom "ab'~o"
rules
[ "a=FF"
"b=?ci6/b"
"c=cF"
"e=&&e"
"i=??6j"
"j=12/[8&eC]"
"C=!cF[9+'D!F`]^^[9-'D!F`]C"
"D=!F[9+F]^[9-F]D"
]}
GaliumOdoratum.gif
LSystem  { name GaliumOdoratum
 info "Galium Odoratum, 8/2005 by Gerd Platl"
angle 3 thickness 4
factor 0.8 deep 8
axiom "'A6LAA8MAA8MD"
rules [ "A=a" "a=FA"
"L=20/[33^!![n]o]" "n=B"
"o=C"
"M=15/[33^!![B]C]" "B=b-B"
"b=[[xg^{F]-x[g.].}]b" "C=c+C"
"c=[[xg^{F]+x[g.].}]c"
"D=?JJJ0%13'~s"
"J=!40/[12^yD]"
"x=g^x"
"y=F^y"
]}


Stochastic L-Systems:

stochastic.gif
Normally all L-systems plants generated by the same L-System are identical, while in reality there is no plant in the world growing in the same way.

Simulating natural process by using probability is a much simpler approach than underlying natural rules. In my new L-System-Interpreter 1.3 you have the possibility to create stochastic L-Systems. You can define more than one rules for only one symbol. If there are more than one rule the LS-Interpreter will choose one of them randomly.

If you generate many virtual plants in a garden, all plants will have different appearance though they are based on the same stochastic L-system definition. As you can see in the example it is a great approximation to nature scene (for example see file Stochastic1.LSY).
LSystem
{ name "StochasticPlant4"
info "stochastic plant 4 with fruit seeds, 12/2005 Gerd Platl"
step 300
thickness 0
factor 0.53
deep 6
axiom F
rules
[ "F=F[+F]F[-F]"
"F=/F[+FJ]F"
"F=\\F[-FH]F"
"H=['-G[GB]-G[GB]-G[GB]-B]"
"J=['+G[GB]+G[GB]+G[GB]+GB]"
"B=[G4'~s]"
]}


Production String Notation:

Basic Commands:
All rules must be defined by using the following commands:
character
default
statement
Befehl (german)
F
step
draw forward
zeichne vorwärts
f
step
jump forward
springe vorwärts
+
angle
turn left
nach links drehen
-
angle
turn right
nach rechts drehen
&
angle
pitch down
nach unten drehen
^
angle
pitch up
nach oben drehen
\
angle
roll left (anticlockwise)
nach links neigen (gegen Uhrzeigersinn)
/
angle
roll right (clockwise)
nach rechts neigen (im Uhrzeigersinn)
|
180°
turn around 180°
um 180° umdrehen
_ 180°
roll 180°
um 180° verdrehen (Kopfstand)
G
step
draw forward
zeichne vorwärts in der Fläche ?
g
step
jump forward
springe vorwärts
{

begin plane
neue Fläche
}

end plane
Fläche beenden
.

add plane point
Flächenpunkt hinzufügen
[

start branch
beginne neuen Zweig
]

complete branch
beende Zweig
'
+1
increment color index
Farbindex erhöhen
!
-1
decrement diameter
Durchmesser verringern
?
0.8
multiply diameter
Durchmesser multiplizieren
#

start line comment
Beginn Zeilenkommentar
*

jump to origin
zum Koordinatenursprung springen
~

add shape (see predefined shapes)
Figur hinzufügen  (siehe Figurentabelle)
>

increment (see increment / decrement)
erhöhen
<

decrement (see increment / decrement)
ernidrigen
$

extended command (see extended commands)
Zusatzkommando
=

assignment seperator
Zuweisungstrennzeichen
<number>
1
repetition / multiplication factor
example  '6+'  means  '++++++'
Wiederholungs- bzw. Multiplikationsfaktor
Beispiel:  '5?'  bedeutet  '?????'





Predefined Shapes:

characters
default
statement
Befehl
~

add shape
Figur hinzufügen  
~c
s = step / 2
add small cube
kleinen Würfel hinzufügen
~C
s = step
add cube
Würfel hinzufügen
~d
d = step / 2
add small disc Scheibe hinzufügen
~D
d = step
add disc Scheibe hinzufügen
~e
d = step,   h=step/2
add flat ellipsoid
flaches Ellipsoid hinzufügen
~E
d = step/2,   h=step
add long ellipsoid längliches Ellipsoid hinzufügen
~l
d = step/2
add small flower Blüte hinzufügen
~L
d = step add flower Blüte hinzufügen
~o
d = step
add small  cone kleinen Kegel hinzufügen
~O
d = step
add cone Kegel hinzufügen
~s
d = step / 2
add small sphere
kleine Kugel  hinzufügen
~S
d = step
add sphere
Kugel hinzufügen
~x
d = step / 2,  h=step
add small cone stump kleinen Kegelstump hinzufügen
~X
d = step,  h=step
add cone stump Kegelstump hinzufügen
~y
d = step / 2,  h=step/2
add small cylinder kleinen Zylinder hinzufügen
~Y
d = step
add cylinder großen Zylinder hinzufügen
~1
d = step
add sprite 1
Sprite Nr.1 hinzufügen
~2
d = step
add sprite 2
Sprite Nr.2 hinzufügen
~3
d = step
add sprite 3
Sprite Nr.3 hinzufügen
~4
d = step
add sprite 4
Billboard-Sprite Nr.4 hinzufügen

Increment / Decrement Commands:

decrement
increment
statement
Befehl
<
>
decrement ... / increment ... erniedrigen ...  / erhöhen...
<a >a angle - 1°  /    angle + 1° Winkel - 1°   /   Winkel + 1°
<A >A  angle * 0.9   / angle * 1.1
Winkel * 0.9   /   Winkel * 1.1
<s
>s
step - 1   /   step + 1
Schrittweite - 1    /   Schrittweite +1
<S
>S
step * 0.9   /   step * 1.1
Schrittweite * 0.9   /   Schrittweite * 1.1
<t
>t
thickness - 1   /   thickness + 1
Dicke - 1   /   Dicke + 1
<T
>T
thickness * 0.9   /   thickness * 1.1
Dicke * 0.9   /   Dicke * 1.1
<c
>c
color index - 1   /   color index + 1
Farbindex - 1   /   Farbindex + 1
<r
>r
tropism - 1   /   tropism + 1
Anziehung - 1   /   Anziehung + 1





Extented Commands

characters default
statement
Befehl
$F
step / 2
draw forward half step zeichne halben Schritt nach vor
$f
step / 2 jump forward half step halben Schritt nach vor springen
$G
step / 2 draw forward half step without planepoint zeichne halben Schritt nach vor
ohne einen Flächenpunkt hinzuzufügen
$g
step / 2 jump forward half step without planepoint
halben Schritt nach vor springen
ohne einen Flächenpunkt hinzuzufügen
$U thick / 2
jump up thickness radius um Dickenradius nach unten springen
$D thick / 2 jump down thickness radius um Dickenradius nach oben springen
$R
thick / 2 jump right thickness radius
um Dickenradius nach rechts springen
$L
thick / 2 jump left thickness radius
um Dickenradius nach links springen
$|
180°
turn around 180° horizontal
um 180° umdrehen
$_
180°
roll 180°
um 180° verdrehen (Kopfstand)
$&
v=-90°
pitch down to vertical
vertikal nach unten drehen
$h
h=0°
roll to horizontal
horizontal ausrichten
$*

jump to origin
zum Ausgangspunkt zurückspringen

Other Applications:

name version
date
OS / source
requirements
author
link

3D L-Systems

?
2001
Windows /  C++
Direct3D
3d LSystem Application by J. Scott Cameron
The College of Wooster 
http://www.alesdar.org/oldSite/IS/chap4-4.html

BioSchematics

0.4.6
7/2005
Linux / C
OpenGL / Guile 1.6
3d L-System interpreter by Xavier Raynaud
http://bioschematics.tuxfamily.org/
Lindenmayer Fraktale
2.2
11/2003
Windows /  (Delphi4)
 ---
2d LSystem-Application by Ulrich Schwebinghaus
http://www.fraktalwelt.de/myhome/lmayer.htm
Lindenmayer II
?
2005
Web-Browser /  Java
JRE
interactive 2d LSystem-Applet by Ulrich Schwebinghaus
http://www.fraktalwelt.de/myhome/lmayer2-g.htm#applet
LParser2
1.0
1/2005
Windows (DOS) / ---
Browser VRML-Plugin
3d LSystems Generator for WRL files by Laurens Lapré
http://home.wanadoo.nl/laurens.lapre
L-Studio 4
4.0.5
2005
Windows 95/NT or later
(Microsoft Visual C++ v.6.0)
OpenGL
3d LSystem Application by Radoslaw Karwowski & Brendan Lane
Department of Computer Science, University of Calgary
http://algorithmicbotany.org/lstudio/
LSYS32
6/1998
Windows / ---

graphical shell for for Laurens Lapre's Lindenmayer system parser
http://chris.lichti.org/Lab/LSys32/LSys32.shtml
LSE
L-System Explorer

1.1
9/2002
Windows / C++
---
2d LSystem-Application by James Matthews
http://www.generation5.org/content/2002/lse.asp
L-Systems Plant
Geometry Generator

?
1999
Macintosh / ---
?
2d LSystem-Application by Bryan Horling
http://shakti.trincoll.edu/~bhorling/lsystems/
L-Systems Applet
1.0
?
Web-Browser /  Java
JRE
interactive 2d LSystem-Applet by Robert Jessop
http://home.clara.net/niknak/fractal/
L-System 4
4.01
7/2000
Windows / ---
---
3d LSystem Application by Timothy C. Perz
http://www.geocities.com/tperz/L4Home.htm
Virtual Plants
1.0
12/1999
Web-Browser / Java
JRE 1.2, Java3d
3d LSystem Application by Rene Gressly
University of Applied Sciences, Biel, Switzerland
http://www.hta-bi.bfh.ch/~swc/DemoJ3D/VirtualPlants/






Links:
2d:
An Introduction to Lindenmayer Systems  
Fractal curves 
Fractint L-Systems   Tutorial by William McWorter 
Ulli's Fractal Home - LSystems 
3d:
Algorithmic Botany at University of Calgary 
Virtual Plants at University Hamburg 
greenworks organic softare - XFrog 
Lparser: Laurens Lapré's Projects 
L-System 4 by Timothy C. Perz  
How to build LS files Tutorial  
Virtual Plants
 
Books:
Book: The Algorithmic Beauty of Plants
Book:   The Algorithmic Beauty of Plants
by Przemyslaw Prusinkiewicz and Aristid Lindenmayer
Springer-Verlag in 1990       (ISBN 0-387-97297-8)
You can download the entire book as a PDF file with high quality (17MB) or low quality (4 Mb).



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