# 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]);
``````