Lindenmayer L-Systems Rules

Creating turtle fractal art with L-Systems just for the fun

These fractals are created with my free L-System app that you can download here:

First install Python 3.8 for Windows :

http://www.qchartist.net/files/programming/fractals/python-3.8.0.exe

Then extract this zip file in a folder inside your Python38-32 folder :

http://www.qchartist.net/files/programming/fractals/lsystem-master_RQ_Py.zip

Enjoy!

https://www.deviantart.com/jul-zen

Hive

Axiom: F

Production 1: F

Rule 1: +F++DF++D[F]D+

Production 2: D

Rule 2: D

Iterations: 7

Angle: 30

von Koch – acute snowflake

axiom=”F+(120)F+(120)F”

rules={“F”: “F-F++F-F”}

iters=4

angle=75

Cesaro curve #1

axiom=”F+(90)F+(90)F+(90)F”

rules={“F”: “F+F–F+F”}

iters=5

angle=85.3

Mango Leaf

axiom=”Y—Y”

rules={“X”: “F-FF-F–[–X]F-FF-F–F-FF-F–“, “Y”: “f-F+X+F-fY”}

iters=10

angle=60

Weed, P. Bourke

axiom=”F”

rules={“F”: “FF-[XY]+[XY]”,”X”:”+cFY”,”Y”:”-dFX”,”c”:””,”d”:””}

iters=6

angle=22.5

poetasters weed, after, P. Bourke

axiom=”F”

rules={“F”: “F-[XY]+[XY]F+[XY]-[XY]”,”X”:”+dFY”,”Y”:”-cFX”,”c”:””,”d”:””}

iters=6

angle=22.5

Unlikely bush (after Bourke)

axiom=”F”

rules={“F”: “eF[+cFF][-FF]cF[-F]d[+F]F”,”c”:””,”d”:””,”e”:””}

iters=3

angle=330

von Koch – islands and lakes

axiom=”F+F+F+F”

rules={“F”: “F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF”, “f”: “ffffff”}

iters=2

angle=90

2D bush #9

axiom=”G”

rules={“G”: “GfX[+G][-G]”, “X”: “X[-FFF][+FFF]FX”}

iters=5

angle=25.71

Snake Kolam

axiom=”F+XF+F+XF”

rules={“X”: “XF-F-F+XF+F+XF-F-F+X”}

iters=4

angle=90

peano_gosper_curve_1

axiom=”FX”

rules={“X”: “X+YF++YF-FX–FXFX-YF+”, “Y”: “-FX+YFYF++YF+FX–FX-Y”}

iters=4

angle=60

segments 1

axiom=”FB”

rules={“A”: “FBFA+HFA+FB-FA”, “B”: “FB+FA-FB-JFBFA”, “H”: “-“, “J”: “+”, “F”: “”}

iters=5

angle=90

Tree

axiom=”X”

rules={“F”: “FF”, “X”: “F-[[X]+X]+F[+FX]-X”}

iters=6

angle=22.5

Wheel

axiom=”WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW”

rules={“W”: “[X]+”, “X”: “[+++++++++++++Y[X]]————-Y[X]”, “Y”: “YFYF”}

iters=8

angle=5

Tree 2

axiom=”FFFFFFX”

rules={“F”: “F”, “X”: “FFF-[-F+F[Y]-[X]]+[+F+F[X]-[X]]”, “Y”: “FF-[-F+F]+[+F+FY]”}

iters=6

angle=15

P. Bourke after Saupe

axiom=”VZFFF”

rules={“V”: “[+++W][—W]YV”,”W”:”+X[-W]Z”,”X”:”-W[+X]Z”,”Y”:”YZ”,”Z”:”[-FcFF][+FdFF]F”,”c”:””,”d”:””}

iters=8

angle=20

poetasters succulent 1

axiom=”A”

rules={“A”: “[FL]gAhg[FLA]”,”F”:”cSF”,”S”:”dFL”,”L”:”c[F+F+F]fe[F-F-F]”,”c”:””,”d”:””,”e”:””,”g”:””,”h”:””}

iters=7

angle=17

Pean-c flower after Gary Teachout

axiom=”FXhFXiFX”

rules={“F”: “”,”X”:”[FX-FY][-cFX-FY-FX][ZZ]-dFY-FX+FY+FX”,”Y”:”FY”,”Z”:”-cFX-FY-FX”,”c”:””,”d”:””,”h”:””,”i”:””}

iters=3

angle=340