If you look at a tree, it is not too hard to imagine that a branch of the tree looks very much like a smaller version of the whole tree. The L-system below uses this idea to model a (tumble?)weed.
Weed {
Angle 50
Axiom +++++++++++++x
x=f[@.5+++++++++x]-f[@.4-----------!x]@.6x
}
The symbols "+", "-", "f", "@", "[", "]", and "!" are reserved symbols in FRACTINT L-Systems. The symbol "x", on the other hand, has no graphic meaning for the FRACTINT L-System interpreter. "x" is just a cell that subdivides into the cells according to the string that follows "x=".
The symbol "+" means "turn left 7.2=360/50 degrees". The symbol "-" means "turn right 7.2 degrees". The text line "Angle 50" tells FRACTINT how much a turn is, namely 360/50 degrees. The symbol "f" means "draw a line in the current direction". The symbols "[" and "]" work together. "[" means "remember the current graphics state, position, orientation, line length, etc." "]" means "set the graphics state back to the remembered state". The symbol "@" means "multiply the current line length by the amount following". Hence "@.5" means multiply the current line length by .5. The symbol "!" means "reverse the meaning of + and-". Now let's translate this L-system into English.
The symbol "x" represents the weed. The Axiom line tells FRACTINT to turn the weed left 13*7.2=93.6 degrees. Since FRACTINT always begins oriented East, this command puts the weed just about upright.
The replacement string for the weed x says draw a line (f), the stem of the weed. Next, shrink the weed by .5, turn left 9*7.2=64.8 degrees, draw the shrunken weed, and return to the stem ([@.5+++++++++x]). This draws the lowest branch of the weed. Next, turn right slightly (7.2 degrees) and draw another portion of the stem (-f). Continuing, shrink the weed by .4, turn right 11*7.2=79.2 degrees, reverse the meaning of right and left, draw the shrunken weed, and return to the stem ([@.4-----------!x]). Finally, draw the weed at .6 size (@.6x). Here is how the Weed L-system looks.
(drawing of Weed using the displayed script)
The L-system files fractint.l and plants.l have many L-systems representing plants. Here are two.
Plant04 { ; Adrian Mariano, from the Algorithmic Beauty of Plants
; Plant-like structure, figure 1.24d p.25
angle 18
axiom x
X=F[+X]F[-X]+X
F=FF
}
(drawing of plant4)
Bush { ; Adrian Mariano
Angle 16
Axiom ++++F
F=FF-[-F+F+F]+[+F-F-F]
}
(drawing of Bush)
Besides normal plants, there are other-worldly organisms that L-systems can model. Here is one modeling a hairy alien.
Alien {
Angle 11
Axiom x
x=[@q2@I2-fx]g[@q2@I2---fx]
f=
}
The symbol combination "@q" means "multiply the line length by the square root of the following number". The symbol combination "@I" means "multiply the line length by the reciprocal of the following number". The symbol "g" means "move forward instead of drawing".
You might ask why I chose the number "Angle 11" and the string "@q2@I2". For perverse reasons. If you merely replace "Angle 11" by "Angle 8", the resulting L-system produces the famous Dragon curve which is described in a more conventional way later in this tutorial. Another reason I selected this L-system is to suggest to you that, to a limited extent, L-systems can create pictures like those produced by IFS systems (which FRACTINT can also handle directly). Anyway, here is a picture of Alien.
(drawing of Alien)
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