FractalGrammars.html

Graphical modeling using L-systems

Some edge rewriting rules:

Quadratic Koch Island
angle = 90
S -> F-F-F-F
F -> F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F

A Quadratic Modification of the Snowflake Curve
angle = 90
S -> -F
F -> F+F-F-F+F

Combination of Islands and Lakes I
angle = 90
S -> F+F+F+F
F -> F+F-F-F+F

A Sequence of Koch Curves obtained by successive modification of the production successor:
(a)
angle = 90
S -> F-F-F-F
F -> FF-F-F-F-F-F+F

(b)
angle = 90
S -> F-F-F-F
F -> FF-F-F-F-FF

(c)
angle = 90
S -> F-F-F-F
F -> FF-F+F-F-FF

(d)
angle = 90
S -> F-F-F-F
F -> FF-F--F-F

(e)
angle = 90
S -> F-F-F-F
F -> F-FF--F-F

(f)
angle = 90
S -> F-F-F-F
F -> F-F+F-F-F

The Dragon Curve:
angle = 90
S -> L
L -> L+R+
R -> -L-R

The Sierpinski Gasket:
angle = 60
S -> R
L -> R+L+R
R -> L-R-L

FASS Curves (space-f illing, self-a voiding, s imple, and self-s imilar):

Hexagonal Gosper Curve:
angle = 60
S -> L
L -> L+R++R-L--LL-R+
R -> -L+RR++R+L--L-R

Quadratic Gosper Curve:
angle = 90
S -> -R
L -> LL-R-R+L+L-R-RL+R+LLR-L+R-LL+R-LR-R-L+L+RR-
R -> +LL-R-R+L+LR+L-RR-L-R+LRR-L-RL+L+R-R-L+L+RR

Combination of Islands and Lakes II:
angle = 90
S -> F+F+F+F
F -> F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF
f -> ffffff

The URL for this document is: http://www.ccs.neu.edu/home/fell/COM1101/HW/PROG/FractalGrammars.html