L-Systems are described in the following book:
Available software:
Koch snowflake
seed F + + F + + F # Initial sequence of symbols rule F -> F - F + + F - F # Symbol rewrite rule delta 60 # Angle of rotation in degrees theta 60 # Initial angel in degrees leng 400 # Length of line element iter 3 # Number of iterations ratio 3 # Scaling of length/iteration x 0 # Initial horizontal position y -235 # Initial vertical position
Shrub
ignore X # X will be ignored seed X rule F -> F F rule X -> F [+ X] F [+ X] - X delta 22.5 theta 90 leng 230 iter 6 ratio 2 x 0 y -230 red 0.0 # color component between 0 and 1 green 0.6 # blue 0.2 #
Islands
move f # f produces invisible line seed F + F + F + F rule F -> F+f-FF+F+FF+Ff+FF-f+FF-F-FF-Ff-FFF rule f -> f f f f f f delta 90 theta 90 leng 236 iter 2 ratio 6 x 128 y -128
Any letter may be used as a non-terminal. For any used letter, there has to be a a corresponding rule. The program is case sensitive for letters used in rules and seed.
Use of color is optional.
Use of ratio is optional (default = 1). The value of leng is divided by ratio^{iter}. For many (but not all) figures, ratio can be defined such that, when the value for iter is altered, no other values need to be adjusted.
F(x) -> F(x * 1.41)
F(x < .5) -> F(x * 1.41) F(x >= .5) -> [ + F(x)] - F(x)
F(.8, .2) -> F -> [ - F ] [ + F ] F