lsystem2


lsystem2 is a 2D implementation of L-system. It's based on the algorithm of turtle grahpics. Instructions for generation of rules are as follows:

F  Move forward and draw line
f  Move forward without drawing a line
+  Turn left
-  Turn right 
|  Reverse direction (ie: turn by 180 degrees)
[  Push current turtle state onto stack
]  Pop current turtle state from the stack

Since: 2.4

Parameters

  • axiom : The initial state of the system.
  • rules : A list of production rules. The first element of each rule is the predecessor, and the second is the successor.
  • n : Iteration times.
  • angle : Used when turing.
  • leng : Used when forwarding. Default to 1.
  • heading : The initial angle of the turtle. Default to 0.
  • start : The starting point of the turtle. Default to [0, 0].
  • forward_chars : Chars used for forwarding after the last iteration. Default to 'F'.
  • rule_prs : The probabilities for taking rules. If each rule is chosen with a certain probability, it's a stochastic L-system. Each probability value for a rule ranges from 0 to 1.
  • seed : Optional. Seed value for random number generator for repeatable results. Since: 3.3.

Examples

lsystem2-collections.scad collects several L-system grammars. Here's one of them.

use <turtle/lsystem2.scad>
use <line2d.scad>

for(line = fern()) {
    line2d(
        line[0],
        line[1],
        .2,
        p1Style = "CAP_ROUND", 
        p2Style =  "CAP_ROUND"
    );
}

function fern(n = 8, angle = 4, leng = 1, heading = 0, start = [0, 0]) = 
    let(
        axiom = "EEEA",
        rules = [
            ["A", "[++++++++++++++EC]B+B[--------------ED]B+BA"],
            ["C", "[---------EE][+++++++++EE]B+C"],
            ["D", "[---------EE][+++++++++EE]B-D"]
        ]
    )
    lsystem2(axiom, rules, n, angle, leng, heading, start, forward_chars = "ABCDE");

lsystem2

// a stochastic L-system

use <turtle/lsystem2.scad>
use <line2d.scad>

for(line = weed()) {
    line2d(
        line[0],
        line[1],
        .2,
        p1Style = "CAP_ROUND", 
        p2Style =  "CAP_ROUND"
    );
}

function weed(n = 6, angle = 22.5, leng = 1, heading = 0, start = [0, 0]) = 
    let(
        axiom = "F",
        rules = [
            ["F", "FF-[XY]+[XY]"],
            ["X", "+FY"],
            ["Y", "-FX"]
        ]
    )
    lsystem2(axiom, rules, n, angle, leng, heading, start, rule_prs = [0.8, 0.8, 0.8]);

lsystem2

lsystem2