# 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.

## Examples

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

``````use <turtle/lsystem3.scad>;

for(line = hilbert_curve()) {
polyline_join([line, line])
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

for(line = vine()) {
polyline_join([line, line])
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]);
``````  