1include <BOSL2/std.scad>
2
3function _lsystem_recurse(s, rules, lev) =
4 lev<=0? s : _lsystem_recurse([
5 for (
6 i = 0,
7 slen = len(s),
8 sout = "";
9
10 i <= slen;
11
12 ch = s[i],
13 found = search([ch], rules)[0],
14 sout = str(sout, i==slen? "" : found==[]? ch : rules[found][1]),
15 i = i + 1
16 ) if (i==slen) sout
17 ][0], rules, lev-1);
18
19
20function _lsystem_to_turtle(s, step=1, angle=90, startang=0) =
21 concat(
22 startang? ["left", startang] : [],
23 ["angle", angle, "length", step],
24 [
25 for (
26 i = 0,
27 slen = len(s);
28
29 i <= slen;
30
31 ch = s[i],
32 cmd = (ch=="A" || ch=="B" || ch=="F")? ["move"] :
33 (ch=="+")? ["left"] :
34 (ch=="-")? ["right"] :
35 [],
36 i=i+1
37 ) if(i>0 && cmd!=[]) each cmd
38 ]
39 );
40
41
42function lsystem_turtle(basis, rules, levels=5, step=1, angle=90, startang=0) =
43 turtle(_lsystem_to_turtle(_lsystem_recurse(basis, rules, levels), step=step, angle=angle, startang=startang));
44
45
46function dragon_curve (levels=9, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "FX", [["X", "X+YF+"], ["Y", "-FX-Y"]]);
47function terdragon_curve (levels=7, step=1) = lsystem_turtle(levels=levels, step=step, angle=120, "F", [["F", "F+F-F"]]);
48function twindragon_curve (levels=11, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "FX+FX+", [["X", "X+YF"], ["Y","FX-Y"]]);
49function moore_curve (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "LFL+F+LFL", [["L", "-RF+LFL+FR-"], ["R", "+LF-RFR-FL+"]]);
50function hilbert_curve (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "X", [["X","-YF+XFX+FY-"], ["Y","+XF-YFY-FX+"]]);
51function gosper_curve (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=60, "A", [["A", "A-B--B+A++AA+B-"], ["B", "+A-BB--B-A++A+B"]]);
52function quadratic_gosper (levels=2, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "-YF", [["X", "XFX-YF-YF+FX+FX-YF-YFFX+YF+FXFXYF-FX+YF+FXFX+YF-FXYF-YF-FX+FX+YFYF-"], ["Y", "+FXFX-YF-YF+FX+FXYF+FX-YFYF-FX-YF+FXYFYF-FX-YFFX+FX+YF-YF-FX+FX+YFY"]]);
53function peano_curve (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "X", [["X","XFYFX+F+YFXFY-F-XFYFX"], ["Y","YFXFY-F-XFYFX+F+YFXFY"]]);
54function koch_snowflake (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=60, "F++F++F", [["F","F-F++F-F"]]);
55function sierpinski_arrowhead(levels=6, step=1) = lsystem_turtle(levels=levels, step=step, angle=60, "A", [["A", "B-A-B"], ["B","A+B+A"]]);
56function sierpinski_triangle (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=120, "A-B-B", [["A","A-B+A+B-A"], ["B","BB"]]);
57function square_sierpinski (levels=5, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "F+XF+F+XF", [["X","XF-F+F-XF+F+XF-F+F-X"]]);
58function cesaro_curve (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=85, "F", [["F","F+F--F+F"]]);
59function paul_bourke1 (levels=3, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "F+F+F+F+", [["F","F+F-F-FF+F+F-F"]]);
60function paul_bourke_triangle(levels=6, step=1) = lsystem_turtle(levels=levels, step=step, angle=120, "F+F+F", [["F","F-F+F"]]);
61function paul_bourke_crystal (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "F+F+F+F", [["F","FF+F++F+F"]]);
62function space_filling_tree (levels=4, step=1) = lsystem_turtle(levels=levels, step=step, angle=90, "X", [["X","FX++F-FX++F-FX++F-FX++F-"],["F", "FF"]], startang=45);
63function krishna_anklets (levels=6, step=1) = lsystem_turtle(levels=levels, step=step, angle=45, "-X--X", [["X","XFX--XFX"]]);
64
65
66points = hilbert_curve(levels=5, step=100/pow(2,5));
67stroke(points, width=1);
68
69
70// vim: expandtab tabstop=4 shiftwidth=4 softtabstop=4 nowrap