`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>;
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]);
```