lsys/lib/fractint.l

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Koch(n) => attr (delta, 360/6) F--F--F, n;
        F       => F+F--F+F;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Koch1(n)        => attr (delta, 360/12) F---F---F---F, n;
        F       => -F+++F---F+;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Koch2(n)        => attr (delta, 360/4) F-F-F-F, n;
        F       => F-F+F+FF-F-F+F;
)

ruleset (       // Adrian Mariano
        Koch3(n)        => attr (delta, 360/4) F+F+F+F, n;
        F       => F-F F+F F+F+F-F-F F+F+F-F-F F-F F+F;

)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Dragon(n)       => attr (delta, 360/8) FX, n;
        F       => ;
        y       => +FX--FY+;
        x       => -FX++FY-;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Peano(n)        => attr (delta, 360/4) F-F-F-F, n;
        F       => F-F+F+F+F-F-F-F+F;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Cesaro(n)       => attr (delta, 360/34) FX, n;
        F       => ;
        X       => ----F!X!++++++++F!X!----;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Double_cesaro(n)        => attr (delta, 360/4) F -(90) F -(90) F -(90) F -(90) , n;
        F       =>  -(42) !F! +(84) !F! -(42) ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot
        anfle   => 6;
        Flow_snake(n)   => attr (delta, 360/4) FL, n;
        L       => FL-FR--FR+FL++FLFL+FR-%,;
        R       => +FL-FRFR--FR-FL++FL+FR%,;
        F       => ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Cantor_dust(n)  => attr (delta, 360/6) F, n;
        F       => FfF;
        f       => fff;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Snowflake(n)    => attr (delta, 360/12) F, n;
        F       => ++!F!F--F--F attr (distance, distance/03^0.5) |+F!F--;
        F       => F--F!+++ attr (distance, distance*03^0.5) F attr (distance, distance/03^0.5) |+F!F attr (distance, distance*03^0.5) |+F!F;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Snowflake_color(n)      => attr (delta, 360/12) F, n;
        F       => --!F!F++F++F attr (distance, distance/03^0.5) |-F!F++;
        F       => F++F!--- attr (distance, distance*03^0.5) F attr (distance, distance/03^0.5) |-F!F attr (distance, distance*03^0.5) |-F!F;
        F       => ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Island(n)       => attr (delta, 360/4) F+F+F+F, n;
        F       => FFFF-F+F+F-F[-fFF+F+FF+F]FF;
        f       =>  attr (distance, distance*08) f attr (distance, distance/08) ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Island1(n)      => attr (delta, 360/4) F+F+F+F, n;
        F       => F+f F-F F-F-F F+f+F F-f F+F F+F+F F-f-F FF;
        f       =>  attr (distance, distance*06) f attr (distance, distance/06) ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Quartet(n)      => attr (delta, 360/4) F b, n;
        A       => FBFA+HFA+FB-FA;
        B       => FB+FA-FB-JFBFA;
        F       => ;
        H       => -;
        J       => +;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Snow_flake(n)   => attr (delta, 360/12) FR, n;
        R       => ++!FRFU++FU++FU!--- attr (distance, distance*03^0.5) FU|- attr (distance, distance/03^0.5) !FRFU!;
        U       => !FRFU!|+ attr (distance, distance*03^0.5) FR attr (distance, distance/03^0.5) +++!FR--FR--FRFU!--;
        F       => ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Snow_flake1(n)  => attr (delta, 360/12) F x, n;
        x       => ++F!x!F y--F x--F y|+ attr (distance, distance/03^0.5) F yF!x!++F!y!++F!y!F x attr (distance, distance*03^0.5) +++F!y!F x;
        y       => F yF!x!+++ attr (distance, distance/03^0.5) F yF!x!++F!x!++F!y!F x attr (distance, distance*03^0.5) |+F x--F y--F xF!y!++;
        F       => ;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot
        anfle   => 12;
        Tree(n) => attr (delta, 360/12) +++FX, n;
        X       =>  attr (distance, distance*0.6) [-FX]+FX;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Peano1(n)       => attr (delta, 360/8) FXY++F++FXY++F, n;
        X       => XY attr (distance, distance*02^0.5) -F attr (distance, distance/02^0.5) -FXY++F++FXY;
        Y       => - attr (distance, distance*02^0.5) F- attr (distance, distance/02^0.5) FXY;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Sierpinski(n)   => attr (delta, 360/3) F, n;
        F       => FXF;
        X       => +FXF-FXF-FXF+;
)

ruleset (       // Adrian Mariano
        // from The Fractal Geometry of Nature by Mandelbrot

        Koch4(n)        => attr (delta, 360/12) F++++F++++F, n;
        F       => +F--F++F-;
)


ruleset (       // Ken Philip, from The Science of Fractal Images p.285b
        Plant(n)        => attr (delta, 360/12) Z, n;
        z       => zFX[+Z][-Z];
        x       => x[-FFF][+FFF]FX;

)

ruleset (       // Ken Philip, from The Science of Fractal Images, p.286
        Plant1(n)       => attr (delta, 360/14) SLFFF, n;
        s       => [+++Z][---Z]TS;
        z       => +H[-Z]L;
        h       => -Z[+H]L;
        t       => TL;
        l       => [-FFF][+FFF]F;

)

ruleset (       // Ken Philip, from The Science of Fractal Images
        Hilbert(n)      => attr (delta, 360/20) x, n;
        x       => -YF+XFX+FY-;
        y       => +XF-YFY-FX+;

)

ruleset (       // From Jim Hanan via Corbit
        Sierpinski1(n)  => attr (delta, 360/4) F-F-F, n;
        F       => F[-F]F;

)


ruleset (
        Peano2(n)       => attr (delta, 360/3) x, n;
        x       => XFYFX+F+YFXFY-F-XFYFX;
        y       => YFXFY-F-XFYFX+F+YFXFY;

)

ruleset (
        Koch5(n)        => attr (delta, 360/4) F+F+F+F, n;
        F       => F+F-F-FFF+F+F-F;

)

ruleset (       // from The Science of Fractal Images
        Sierpinski2(n)  => attr (delta, 360/4) FXF--FF--FF, n;
        F       => FF;
        x       => --FXF++FXF++FXF--;

)

ruleset (
        Sierpinski_square(n)    => attr (delta, 360/6) F+F+F+F, n;
        F       => FF+F+F+F+FF;

)


ruleset (       // created by Adrian Mariano

        Pentagram(n)    => attr (delta, 360/10) F x++F x++F x++F x++F x, n;
        // f=f[++++@1.618033989f]
        x       => [++++ attr (distance, distance/01.618033989) F attr (distance, distance*0.618033989) F!x! attr (distance, distance/0.618033989) F];
)


ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Quadratic Koch island, Figure 1.7a p.9

        Quad_koch(n)    => attr (delta, 360/4) F-F-F-F-, n;
        F       => F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // FASS curve (3x3 tiles form macrotile), Figure 1.16a p.17
        Fass(n) => attr (delta, 360/4) -l, n;

        L       => LF+RFR+FL-F-LFLFL-FRFR+;
        R       => -LFLF+RFRFR+F+RF-LFL-FR;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // FASS curve (4x4 tiles form macrotile), Figure 1.16b p.17

        Fass1(n)        => attr (delta, 360/4) -l, n;
        L       => LFLF+RFR+FLFL-FRF-LFL-FR+F+RF-LFL-FRFRFR+;
        R       => -LFLFLF+RFR+FL-F-LF+RFR+FLF+RFRF-LFL-FRFR;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Quadratic Gosper curve, Figure 1.11b p.12

        Quad_gosper(n)  => attr (delta, 360/4) -F r, n;
        l       => F lF l-F r-F r+F l+F l-F r-F rF l+F r+F lF lF r-F l+F r+F lF l+F r-F lF r-F r-F l+F l+F rF r-;
        r       => +F lF l-F r-F r+F l+F lF r+F l-F rF r-F l-F r+F lF rF r-F l-F rF l+F l+F r-F r-F l+F l+F rF r;
        F       => ;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Plant-like structure, figure 1.24a p.25
        // also p.285a The Science of Fractal Images

        Plant2(n)       => attr (delta, 360/14) F, n;
        F       => F[+F]F[-F]F;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Plant-like structure, figure 1.24b p.25

        Plant3(n)       => attr (delta, 360/18) F, n;
        F       => F[+F]F[-F][F];
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Plant-like structure, figure 1.24c p.25

        Plant4(n)       => attr (delta, 360/16) F, n;
        F       => FF-[-F+F+F]+[+F-F-F];
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Plant-like structure, figure 1.24d p.25

        Plant5(n)       => attr (delta, 360/18) x, n;
        X       => F[+X]F[-X]+X;
        F       => FF;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Plant-like structure, figure 1.24e p.25

        Plant6(n)       => attr (delta, 360/14) x, n;
        X       => F[+X][-X]FX;
        F       => FF;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Plant-like structure, figure 1.24f p.25

        Plant7(n)       => attr (delta, 360/16) x, n;
        X       => F-[[X]+X]+F[+FX]-X;
        F       => FF;
)

ruleset (       // Adrian Mariano
        Plant8(n)       => attr (delta, 360/16) y, n;
        x       => X[-FFF][+FFF]FX;
        y       => YFX[+Y][-Y];

)

ruleset (       // Adrian Mariano
        Plant9(n)       => attr (delta, 360/14) F, n;
        F       => F[+F F][-F F]F[+F F][-F F]F;

)


ruleset (       // Adrian Mariano
        Plant10(n)      => attr (delta, 360/10) F, n;
        F       => F[+F[+F][-F]F][-F[+F][-F]F]F[+F][-F]F;

)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // curve from figure 1.9a p.10

        Curve(n)        => attr (delta, 360/4) F-F-F-F-, n;
        F       => FF-F-F-F-F-F+F;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants

        Curve1(n)       => attr (delta, 360/4) F-F-F-F-, n;
        F       => FF-F+F-F-FF;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // curve from figure 1.9e p.10
        Curve2(n)       => attr (delta, 360/4) F-F-F-F-, n;

        F       => F-FF--F-F;
)

ruleset (       // Adrian Mariano
        Curve3(n)       => attr (delta, 360/4) y F, n;
        x       => YF+XF+Y;
        y       => XF-YF-X;

)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Compound leaf with alternating branches, Figure 5.12b p.130

        Leaf(n) => attr (delta, 360/8) x, n;
        a       => n;
        n       => o;
        o       => p;
        p       => x;
        b       => e;
        e       => h;
        h       => j;
        j       => y;
        x       => F[+A(4)]F y;
        y       => F[-B(4)]F x;
        F       =>  attr (distance, distance*01.18) F attr (distance, distance/01.18) ;
)

ruleset (       // Adrian Mariano, from the Algorithmic Beauty of Plants
        // Compound leaf with alternating branches, Figure 5.12a p.130

        Leaf1(n)        => attr (delta, 360/8) a, n;
        a       => F[+x]F b;
        b       => F[-y]F a;
        x       => a;
        y       => b;
        F       =>  attr (distance, distance*01.36) F attr (distance, distance/01.36) ;
)

ruleset (       // Adrian Mariano

        Bush(n) => attr (delta, 360/16) ++++F, n;
        F       => FF-[-F+F+F]+[+F-F-F];
)

ruleset (       // Adrian Mariano

        My_tree(n)      => attr (delta, 360/16) ++++F, n;
        F       => FF-[XY]+[XY];
        X       => +FY;
        Y       => -FX;
)

ruleset (       // Adrian Mariano

        Color_triang_gasket(n)  => attr (delta, 360/6) --X, n;
        X       => ++FXF++FXF++FXF;
        F       => FF;
)

ruleset (       // Adrian Mariano

        Square_gasket(n)        => attr (delta, 360/4) X, n;
        X       => +FXF+FXF+FXF+FXF;
        F       => FF;
)

ruleset (       // Adrian Mariano

        Dragon_curve(n) => attr (delta, 360/4) X, n;
        X       => X-YF-;
        Y       => +FX+Y;
)

ruleset (       // Adrian Mariano

        Square(n)       => attr (delta, 360/4) F+F+F+F, n;
        F       => FF+F+F+F+FF;
)

ruleset (       // Adrian Mariano

        Koch_curve(n)   => attr (delta, 360/6) F, n;
        F       => F+F--F+F;
)


ruleset (       // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
        // Roger Penrose's rhombuses

        Penrose(n)      => attr (delta, 360/10) +WF--XF---YF--ZF, n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (       // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
        // Roger Penrose's rhombuses
        // Uses color to show the edge matching rules to force nonperiodicy

        Color_penrose(n)        => attr (delta, 360/10) +WF--XF---YF--ZF, n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (       // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
        // Roger Penrose's rhombuses

        Penrose1(n)     => attr (delta, 360/10) ++ZF----XF-YF----WF, n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (       // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
        // Roger Penrose's rhombuses

        Penrose2(n)     => attr (delta, 360/10) [X]++[X]++[X]++[X]++[X], n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (       // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
        // Roger Penrose's rhombuses

        Penrose3(n)     => attr (delta, 360/10) [Y]++[Y]++[Y]++[Y]++[Y], n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (       // by Herb Savage
        // This is Penrose3 and Penrose4 superimposed

        Double_penrose(n)       => attr (delta, 360/10) [X][Y]++[X][Y]++[X][Y]++[X][Y]++[X][Y], n;
        W       => YF++ZF----XF[-YF----WF]++;
        X       => +YF--ZF[---WF--XF]+;
        Y       => -WF++XF[+++YF++ZF]-;
        Z       => --YF++++WF[+ZF++++XF]--XF;
        F       => ;
)

ruleset (       // by Herb Savage
        // based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers"
        // This is an example of a "reptile"

        Sphinx(n)       => attr (delta, 360/6) X, n;
        X       => +FF-YFF+FF--FFF|X|F--YFFFYFFF|;
        Y       => -FF+XFF-FF++FFF|Y|F++XFFFXFFF|;
        F       => ff;
        f       => ff;
)

ruleset (
        // Manual construction by Roger Penrose as a prelude to his development of
        // the famous Penrose tiles (the kites and darts) that tile the plane
        // only non-periodically.
        // Translated first to a "dragon curve" and finally to an L-system
        // by Joe Saverino.

        Penta_plexity(n)        => attr (delta, 360/10) F++F++F++F++F, n;
        F       => F++F++F|F-F++F;
)

        // old PentaPlexity:
        // Angle 10
        // Axiom F++F++F++F++Fabxjeabxykabxyelbxyeahxyeabiye
        // F=
        // a=Fabxjea
        // b=++F--bxykab
        // x=++++F----xyelbx
        // y=----F++++yeahxy
        // e=--F++eabiye
        // h=+++++F-----hijxlh
        // i=---F+++ijkyhi
        // j=-F+jkleij
        // k=+F-klhajk
        // l=+++F---lhibkl

ruleset (       // Adrian Mariano
        Circular_tile(n)        => attr (delta, 360/10) X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X, n;
        x       => [F+F+F+F[---X-Y]+++++F++++++++F-F-F-F];
        y       => [F+F+F+F[---Y]+++++F++++++++F-F-F-F];

)

Revision:	1.1
Committed:	Thu Nov 6 14:31:25 2008 UTC (15 years, 6 months ago) by root
Branch:	MAIN
CVS Tags:	HEAD
Log Message:	* empty log message *
#	Content
1	ruleset ( // Adrian Mariano
2	// from The Fractal Geometry of Nature by Mandelbrot
3
4	Koch(n) => attr (delta, 360/6) F--F--F, n;
5	F => F+F--F+F;
6	)
7
8	ruleset ( // Adrian Mariano
9	// from The Fractal Geometry of Nature by Mandelbrot
10
11	Koch1(n) => attr (delta, 360/12) F---F---F---F, n;
12	F => -F+++F---F+;
13	)
14
15	ruleset ( // Adrian Mariano
16	// from The Fractal Geometry of Nature by Mandelbrot
17
18	Koch2(n) => attr (delta, 360/4) F-F-F-F, n;
19	F => F-F+F+FF-F-F+F;
20	)
21
22	ruleset ( // Adrian Mariano
23	Koch3(n) => attr (delta, 360/4) F+F+F+F, n;
24	F => F-F F+F F+F+F-F-F F+F+F-F-F F-F F+F;
25
26	)
27
28	ruleset ( // Adrian Mariano
29	// from The Fractal Geometry of Nature by Mandelbrot
30
31	Dragon(n) => attr (delta, 360/8) FX, n;
32	F => ;
33	y => +FX--FY+;
34	x => -FX++FY-;
35	)
36
37	ruleset ( // Adrian Mariano
38	// from The Fractal Geometry of Nature by Mandelbrot
39
40	Peano(n) => attr (delta, 360/4) F-F-F-F, n;
41	F => F-F+F+F+F-F-F-F+F;
42	)
43
44	ruleset ( // Adrian Mariano
45	// from The Fractal Geometry of Nature by Mandelbrot
46
47	Cesaro(n) => attr (delta, 360/34) FX, n;
48	F => ;
49	X => ----F!X!++++++++F!X!----;
50	)
51
52	ruleset ( // Adrian Mariano
53	// from The Fractal Geometry of Nature by Mandelbrot
54
55	Double_cesaro(n) => attr (delta, 360/4) F -(90) F -(90) F -(90) F -(90) , n;
56	F => -(42) !F! +(84) !F! -(42) ;
57	)
58
59	ruleset ( // Adrian Mariano
60	// from The Fractal Geometry of Nature by Mandelbrot
61	anfle => 6;
62	Flow_snake(n) => attr (delta, 360/4) FL, n;
63	L => FL-FR--FR+FL++FLFL+FR-%,;
64	R => +FL-FRFR--FR-FL++FL+FR%,;
65	F => ;
66	)
67
68	ruleset ( // Adrian Mariano
69	// from The Fractal Geometry of Nature by Mandelbrot
70
71	Cantor_dust(n) => attr (delta, 360/6) F, n;
72	F => FfF;
73	f => fff;
74	)
75
76	ruleset ( // Adrian Mariano
77	// from The Fractal Geometry of Nature by Mandelbrot
78
79	Snowflake(n) => attr (delta, 360/12) F, n;
80	F => ++!F!F--F--F attr (distance, distance/03^0.5) \|+F!F--;
81	F => F--F!+++ attr (distance, distance03^0.5) F attr (distance, distance/03^0.5) \|+F!F attr (distance, distance03^0.5) \|+F!F;
82	)
83
84	ruleset ( // Adrian Mariano
85	// from The Fractal Geometry of Nature by Mandelbrot
86
87	Snowflake_color(n) => attr (delta, 360/12) F, n;
88	F => --!F!F++F++F attr (distance, distance/03^0.5) \|-F!F++;
89	F => F++F!--- attr (distance, distance03^0.5) F attr (distance, distance/03^0.5) \|-F!F attr (distance, distance03^0.5) \|-F!F;
90	F => ;
91	)
92
93	ruleset ( // Adrian Mariano
94	// from The Fractal Geometry of Nature by Mandelbrot
95
96	Island(n) => attr (delta, 360/4) F+F+F+F, n;
97	F => FFFF-F+F+F-F[-fFF+F+FF+F]FF;
98	f => attr (distance, distance*08) f attr (distance, distance/08) ;
99	)
100
101	ruleset ( // Adrian Mariano
102	// from The Fractal Geometry of Nature by Mandelbrot
103
104	Island1(n) => attr (delta, 360/4) F+F+F+F, n;
105	F => F+f F-F F-F-F F+f+F F-f F+F F+F+F F-f-F FF;
106	f => attr (distance, distance*06) f attr (distance, distance/06) ;
107	)
108
109	ruleset ( // Adrian Mariano
110	// from The Fractal Geometry of Nature by Mandelbrot
111
112	Quartet(n) => attr (delta, 360/4) F b, n;
113	A => FBFA+HFA+FB-FA;
114	B => FB+FA-FB-JFBFA;
115	F => ;
116	H => -;
117	J => +;
118	)
119
120	ruleset ( // Adrian Mariano
121	// from The Fractal Geometry of Nature by Mandelbrot
122
123	Snow_flake(n) => attr (delta, 360/12) FR, n;
124	R => ++!FRFU++FU++FU!--- attr (distance, distance*03^0.5) FU\|- attr (distance, distance/03^0.5) !FRFU!;
125	U => !FRFU!\|+ attr (distance, distance*03^0.5) FR attr (distance, distance/03^0.5) +++!FR--FR--FRFU!--;
126	F => ;
127	)
128
129	ruleset ( // Adrian Mariano
130	// from The Fractal Geometry of Nature by Mandelbrot
131
132	Snow_flake1(n) => attr (delta, 360/12) F x, n;
133	x => ++F!x!F y--F x--F y\|+ attr (distance, distance/03^0.5) F yF!x!++F!y!++F!y!F x attr (distance, distance*03^0.5) +++F!y!F x;
134	y => F yF!x!+++ attr (distance, distance/03^0.5) F yF!x!++F!x!++F!y!F x attr (distance, distance*03^0.5) \|+F x--F y--F xF!y!++;
135	F => ;
136	)
137
138	ruleset ( // Adrian Mariano
139	// from The Fractal Geometry of Nature by Mandelbrot
140	anfle => 12;
141	Tree(n) => attr (delta, 360/12) +++FX, n;
142	X => attr (distance, distance*0.6) [-FX]+FX;
143	)
144
145	ruleset ( // Adrian Mariano
146	// from The Fractal Geometry of Nature by Mandelbrot
147
148	Peano1(n) => attr (delta, 360/8) FXY++F++FXY++F, n;
149	X => XY attr (distance, distance*02^0.5) -F attr (distance, distance/02^0.5) -FXY++F++FXY;
150	Y => - attr (distance, distance*02^0.5) F- attr (distance, distance/02^0.5) FXY;
151	)
152
153	ruleset ( // Adrian Mariano
154	// from The Fractal Geometry of Nature by Mandelbrot
155
156	Sierpinski(n) => attr (delta, 360/3) F, n;
157	F => FXF;
158	X => +FXF-FXF-FXF+;
159	)
160
161	ruleset ( // Adrian Mariano
162	// from The Fractal Geometry of Nature by Mandelbrot
163
164	Koch4(n) => attr (delta, 360/12) F++++F++++F, n;
165	F => +F--F++F-;
166	)
167
168
169	ruleset ( // Ken Philip, from The Science of Fractal Images p.285b
170	Plant(n) => attr (delta, 360/12) Z, n;
171	z => zFX[+Z][-Z];
172	x => x[-FFF][+FFF]FX;
173
174	)
175
176	ruleset ( // Ken Philip, from The Science of Fractal Images, p.286
177	Plant1(n) => attr (delta, 360/14) SLFFF, n;
178	s => [+++Z][---Z]TS;
179	z => +H[-Z]L;
180	h => -Z[+H]L;
181	t => TL;
182	l => [-FFF][+FFF]F;
183
184	)
185
186	ruleset ( // Ken Philip, from The Science of Fractal Images
187	Hilbert(n) => attr (delta, 360/20) x, n;
188	x => -YF+XFX+FY-;
189	y => +XF-YFY-FX+;
190
191	)
192
193	ruleset ( // From Jim Hanan via Corbit
194	Sierpinski1(n) => attr (delta, 360/4) F-F-F, n;
195	F => F[-F]F;
196
197	)
198
199
200	ruleset (
201	Peano2(n) => attr (delta, 360/3) x, n;
202	x => XFYFX+F+YFXFY-F-XFYFX;
203	y => YFXFY-F-XFYFX+F+YFXFY;
204
205	)
206
207	ruleset (
208	Koch5(n) => attr (delta, 360/4) F+F+F+F, n;
209	F => F+F-F-FFF+F+F-F;
210
211	)
212
213	ruleset ( // from The Science of Fractal Images
214	Sierpinski2(n) => attr (delta, 360/4) FXF--FF--FF, n;
215	F => FF;
216	x => --FXF++FXF++FXF--;
217
218	)
219
220	ruleset (
221	Sierpinski_square(n) => attr (delta, 360/6) F+F+F+F, n;
222	F => FF+F+F+F+FF;
223
224	)
225
226
227	ruleset ( // created by Adrian Mariano
228
229	Pentagram(n) => attr (delta, 360/10) F x++F x++F x++F x++F x, n;
230	// f=f[++++@1.618033989f]
231	x => [++++ attr (distance, distance/01.618033989) F attr (distance, distance*0.618033989) F!x! attr (distance, distance/0.618033989) F];
232	)
233
234
235	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
236	// Quadratic Koch island, Figure 1.7a p.9
237
238	Quad_koch(n) => attr (delta, 360/4) F-F-F-F-, n;
239	F => F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F;
240	)
241
242	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
243	// FASS curve (3x3 tiles form macrotile), Figure 1.16a p.17
244	Fass(n) => attr (delta, 360/4) -l, n;
245
246	L => LF+RFR+FL-F-LFLFL-FRFR+;
247	R => -LFLF+RFRFR+F+RF-LFL-FR;
248	)
249
250	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
251	// FASS curve (4x4 tiles form macrotile), Figure 1.16b p.17
252
253	Fass1(n) => attr (delta, 360/4) -l, n;
254	L => LFLF+RFR+FLFL-FRF-LFL-FR+F+RF-LFL-FRFRFR+;
255	R => -LFLFLF+RFR+FL-F-LF+RFR+FLF+RFRF-LFL-FRFR;
256	)
257
258	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
259	// Quadratic Gosper curve, Figure 1.11b p.12
260
261	Quad_gosper(n) => attr (delta, 360/4) -F r, n;
262	l => F lF l-F r-F r+F l+F l-F r-F rF l+F r+F lF lF r-F l+F r+F lF l+F r-F lF r-F r-F l+F l+F rF r-;
263	r => +F lF l-F r-F r+F l+F lF r+F l-F rF r-F l-F r+F lF rF r-F l-F rF l+F l+F r-F r-F l+F l+F rF r;
264	F => ;
265	)
266
267	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
268	// Plant-like structure, figure 1.24a p.25
269	// also p.285a The Science of Fractal Images
270
271	Plant2(n) => attr (delta, 360/14) F, n;
272	F => F[+F]F[-F]F;
273	)
274
275	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
276	// Plant-like structure, figure 1.24b p.25
277
278	Plant3(n) => attr (delta, 360/18) F, n;
279	F => F[+F]F[-F][F];
280	)
281
282	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
283	// Plant-like structure, figure 1.24c p.25
284
285	Plant4(n) => attr (delta, 360/16) F, n;
286	F => FF-[-F+F+F]+[+F-F-F];
287	)
288
289	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
290	// Plant-like structure, figure 1.24d p.25
291
292	Plant5(n) => attr (delta, 360/18) x, n;
293	X => F[+X]F[-X]+X;
294	F => FF;
295	)
296
297	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
298	// Plant-like structure, figure 1.24e p.25
299
300	Plant6(n) => attr (delta, 360/14) x, n;
301	X => F[+X][-X]FX;
302	F => FF;
303	)
304
305	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
306	// Plant-like structure, figure 1.24f p.25
307
308	Plant7(n) => attr (delta, 360/16) x, n;
309	X => F-[[X]+X]+F[+FX]-X;
310	F => FF;
311	)
312
313	ruleset ( // Adrian Mariano
314	Plant8(n) => attr (delta, 360/16) y, n;
315	x => X[-FFF][+FFF]FX;
316	y => YFX[+Y][-Y];
317
318	)
319
320	ruleset ( // Adrian Mariano
321	Plant9(n) => attr (delta, 360/14) F, n;
322	F => F[+F F][-F F]F[+F F][-F F]F;
323
324	)
325
326
327	ruleset ( // Adrian Mariano
328	Plant10(n) => attr (delta, 360/10) F, n;
329	F => F[+F[+F][-F]F][-F[+F][-F]F]F[+F][-F]F;
330
331	)
332
333	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
334	// curve from figure 1.9a p.10
335
336	Curve(n) => attr (delta, 360/4) F-F-F-F-, n;
337	F => FF-F-F-F-F-F+F;
338	)
339
340	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
341
342	Curve1(n) => attr (delta, 360/4) F-F-F-F-, n;
343	F => FF-F+F-F-FF;
344	)
345
346	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
347	// curve from figure 1.9e p.10
348	Curve2(n) => attr (delta, 360/4) F-F-F-F-, n;
349
350	F => F-FF--F-F;
351	)
352
353	ruleset ( // Adrian Mariano
354	Curve3(n) => attr (delta, 360/4) y F, n;
355	x => YF+XF+Y;
356	y => XF-YF-X;
357
358	)
359
360	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
361	// Compound leaf with alternating branches, Figure 5.12b p.130
362
363	Leaf(n) => attr (delta, 360/8) x, n;
364	a => n;
365	n => o;
366	o => p;
367	p => x;
368	b => e;
369	e => h;
370	h => j;
371	j => y;
372	x => F[+A(4)]F y;
373	y => F[-B(4)]F x;
374	F => attr (distance, distance*01.18) F attr (distance, distance/01.18) ;
375	)
376
377	ruleset ( // Adrian Mariano, from the Algorithmic Beauty of Plants
378	// Compound leaf with alternating branches, Figure 5.12a p.130
379
380	Leaf1(n) => attr (delta, 360/8) a, n;
381	a => F[+x]F b;
382	b => F[-y]F a;
383	x => a;
384	y => b;
385	F => attr (distance, distance*01.36) F attr (distance, distance/01.36) ;
386	)
387
388	ruleset ( // Adrian Mariano
389
390	Bush(n) => attr (delta, 360/16) ++++F, n;
391	F => FF-[-F+F+F]+[+F-F-F];
392	)
393
394	ruleset ( // Adrian Mariano
395
396	My_tree(n) => attr (delta, 360/16) ++++F, n;
397	F => FF-[XY]+[XY];
398	X => +FY;
399	Y => -FX;
400	)
401
402	ruleset ( // Adrian Mariano
403
404	Color_triang_gasket(n) => attr (delta, 360/6) --X, n;
405	X => ++FXF++FXF++FXF;
406	F => FF;
407	)
408
409	ruleset ( // Adrian Mariano
410
411	Square_gasket(n) => attr (delta, 360/4) X, n;
412	X => +FXF+FXF+FXF+FXF;
413	F => FF;
414	)
415
416	ruleset ( // Adrian Mariano
417
418	Dragon_curve(n) => attr (delta, 360/4) X, n;
419	X => X-YF-;
420	Y => +FX+Y;
421	)
422
423	ruleset ( // Adrian Mariano
424
425	Square(n) => attr (delta, 360/4) F+F+F+F, n;
426	F => FF+F+F+F+FF;
427	)
428
429	ruleset ( // Adrian Mariano
430
431	Koch_curve(n) => attr (delta, 360/6) F, n;
432	F => F+F--F+F;
433	)
434
435
436	ruleset ( // by Herb Savage
437	// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
438	// Roger Penrose's rhombuses
439
440	Penrose(n) => attr (delta, 360/10) +WF--XF---YF--ZF, n;
441	W => YF++ZF----XF[-YF----WF]++;
442	X => +YF--ZF[---WF--XF]+;
443	Y => -WF++XF[+++YF++ZF]-;
444	Z => --YF++++WF[+ZF++++XF]--XF;
445	F => ;
446	)
447
448	ruleset ( // by Herb Savage
449	// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
450	// Roger Penrose's rhombuses
451	// Uses color to show the edge matching rules to force nonperiodicy
452
453	Color_penrose(n) => attr (delta, 360/10) +WF--XF---YF--ZF, n;
454	W => YF++ZF----XF[-YF----WF]++;
455	X => +YF--ZF[---WF--XF]+;
456	Y => -WF++XF[+++YF++ZF]-;
457	Z => --YF++++WF[+ZF++++XF]--XF;
458	F => ;
459	)
460
461	ruleset ( // by Herb Savage
462	// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
463	// Roger Penrose's rhombuses
464
465	Penrose1(n) => attr (delta, 360/10) ++ZF----XF-YF----WF, n;
466	W => YF++ZF----XF[-YF----WF]++;
467	X => +YF--ZF[---WF--XF]+;
468	Y => -WF++XF[+++YF++ZF]-;
469	Z => --YF++++WF[+ZF++++XF]--XF;
470	F => ;
471	)
472
473	ruleset ( // by Herb Savage
474	// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
475	// Roger Penrose's rhombuses
476
477	Penrose2(n) => attr (delta, 360/10) [X]++[X]++[X]++[X]++[X], n;
478	W => YF++ZF----XF[-YF----WF]++;
479	X => +YF--ZF[---WF--XF]+;
480	Y => -WF++XF[+++YF++ZF]-;
481	Z => --YF++++WF[+ZF++++XF]--XF;
482	F => ;
483	)
484
485	ruleset ( // by Herb Savage
486	// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers",
487	// Roger Penrose's rhombuses
488
489	Penrose3(n) => attr (delta, 360/10) [Y]++[Y]++[Y]++[Y]++[Y], n;
490	W => YF++ZF----XF[-YF----WF]++;
491	X => +YF--ZF[---WF--XF]+;
492	Y => -WF++XF[+++YF++ZF]-;
493	Z => --YF++++WF[+ZF++++XF]--XF;
494	F => ;
495	)
496
497	ruleset ( // by Herb Savage
498	// This is Penrose3 and Penrose4 superimposed
499
500	Double_penrose(n) => attr (delta, 360/10) [X][Y]++[X][Y]++[X][Y]++[X][Y]++[X][Y], n;
501	W => YF++ZF----XF[-YF----WF]++;
502	X => +YF--ZF[---WF--XF]+;
503	Y => -WF++XF[+++YF++ZF]-;
504	Z => --YF++++WF[+ZF++++XF]--XF;
505	F => ;
506	)
507
508	ruleset ( // by Herb Savage
509	// based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers"
510	// This is an example of a "reptile"
511
512	Sphinx(n) => attr (delta, 360/6) X, n;
513	X => +FF-YFF+FF--FFF\|X\|F--YFFFYFFF\|;
514	Y => -FF+XFF-FF++FFF\|Y\|F++XFFFXFFF\|;
515	F => ff;
516	f => ff;
517	)
518
519	ruleset (
520	// Manual construction by Roger Penrose as a prelude to his development of
521	// the famous Penrose tiles (the kites and darts) that tile the plane
522	// only non-periodically.
523	// Translated first to a "dragon curve" and finally to an L-system
524	// by Joe Saverino.
525
526	Penta_plexity(n) => attr (delta, 360/10) F++F++F++F++F, n;
527	F => F++F++F\|F-F++F;
528	)
529
530	// old PentaPlexity:
531	// Angle 10
532	// Axiom F++F++F++F++Fabxjeabxykabxyelbxyeahxyeabiye
533	// F=
534	// a=Fabxjea
535	// b=++F--bxykab
536	// x=++++F----xyelbx
537	// y=----F++++yeahxy
538	// e=--F++eabiye
539	// h=+++++F-----hijxlh
540	// i=---F+++ijkyhi
541	// j=-F+jkleij
542	// k=+F-klhajk
543	// l=+++F---lhibkl
544
545	ruleset ( // Adrian Mariano
546	Circular_tile(n) => attr (delta, 360/10) X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X, n;
547	x => [F+F+F+F[---X-Y]+++++F++++++++F-F-F-F];
548	y => [F+F+F+F[---Y]+++++F++++++++F-F-F-F];
549
550	)
551