dotSCAD/docs/lib3x-lsystem3.md

lsystem3

lsystem3 is a 3D 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)
&  Pitch down
^  Pitch up
\  Roll left
/  Roll right       
[  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

lsystem3-collections.scad collects several L-system grammars. Here's one of them.

use <turtle/lsystem3.scad>
use <polyline_join.scad>

for(line = hilbert_curve()) {
	polyline_join([line[0], line[1]])
	    sphere(.25, $fn = 4);
}  

function hilbert_curve(n = 3, angle = 90, leng = 1, heading = 0, start = [0, 0, 0]) = 
	let(
		axiom = "A",
		rules = [
			["A", "B-F+CFC+F-D&F^D-F+&&CFC+F+B//"],
			["B", "A&F^CFB^F^D^^-F-D^|F^B|FC^F^A//"],
			["C", "|D^|F^B-F+C^F^A&&FA&F^C+F+B^F^D//"],
			["D", "|CFB-F+B|FA&F^A&&FB-F+B|FC//"]
		]
	)
	lsystem3(axiom, rules, n, angle, leng, heading, start);  

// a stochastic L-system

use <turtle/lsystem3.scad>
use <polyline_join.scad>

for(line = vine()) {
	polyline_join([line[0], line[1]])
	    sphere(.25, $fn = 4);
}  

function vine(n = 3, angle = 18, leng = 1, heading = 0, start = [0, 0, 0]) = 
	let(
		axiom = "--F",
		rules = [
			["F", "/F[++F]-\\F[--F]+//F"]
		]
	)
	lsystem3(axiom, rules, n, angle, leng, heading, start, rule_prs = [0.8]);