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79 lines
2.5 KiB
Markdown
79 lines
2.5 KiB
Markdown
# lsystem3
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`lsystem3` is a 3D implementation of [L-system](https://en.wikipedia.org/wiki/L-system). It's based on the algorithm of turtle grahpics. Instructions for generation of rules are as follows:
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F Move forward and draw line
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f Move forward without drawing a line
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+ Turn left
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- Turn right
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| Reverse direction (ie: turn by 180 degrees)
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& Pitch down
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^ Pitch up
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\ Roll left
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/ Roll right
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[ Push current turtle state onto stack
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] Pop current turtle state from the stack
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**Since:** 2.4
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## Parameters
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- `axiom` : The initial state of the system.
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- `rules` : A list of production rules. The first element of each rule is the predecessor, and the second is the successor.
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- `n` : Iteration times.
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- `angle` : Used when turing.
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- `leng` : Used when forwarding. Default to `1`.
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- `heading` : The initial angle of the turtle. Default to `0`.
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- `start` : The starting point of the turtle. Default to `[0, 0]`.
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- `forward_chars` : Chars used for forwarding after the last iteration. Default to `'F'`.
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- `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.
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- `seed` : Optional. Seed value for random number generator for repeatable results. **Since:** 3.3.
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## Examples
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[lsystem3-collections.scad](https://github.com/JustinSDK/dotSCAD/blob/master/examples/turtle/lsystem3_collection.scad) collects several L-system grammars. Here's one of them.
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use <turtle/lsystem3.scad>
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use <polyline_join.scad>
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for(line = hilbert_curve()) {
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polyline_join([line[0], line[1]])
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sphere(.25, $fn = 4);
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}
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function hilbert_curve(n = 3, angle = 90, leng = 1, heading = 0, start = [0, 0, 0]) =
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let(
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axiom = "A",
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rules = [
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["A", "B-F+CFC+F-D&F^D-F+&&CFC+F+B//"],
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["B", "A&F^CFB^F^D^^-F-D^|F^B|FC^F^A//"],
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["C", "|D^|F^B-F+C^F^A&&FA&F^C+F+B^F^D//"],
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["D", "|CFB-F+B|FA&F^A&&FB-F+B|FC//"]
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]
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)
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lsystem3(axiom, rules, n, angle, leng, heading, start);
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// a stochastic L-system
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use <turtle/lsystem3.scad>
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use <polyline_join.scad>
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for(line = vine()) {
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polyline_join([line[0], line[1]])
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sphere(.25, $fn = 4);
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}
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function vine(n = 3, angle = 18, leng = 1, heading = 0, start = [0, 0, 0]) =
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let(
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axiom = "--F",
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rules = [
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["F", "/F[++F]-\\F[--F]+//F"]
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]
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)
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lsystem3(axiom, rules, n, angle, leng, heading, start, rule_prs = [0.8]);
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