dotSCAD/docs/lib2x-lsystem2.md

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.

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");  

// 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]);