Koch1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 6 Axiom F--F--F F=F+F--F+F } Koch2 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 12 Axiom F---F---F---F F=-F+++F---F+ } Koch3 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 4 Axiom F-F-F-F F=F-F+F+FF-F-F+F } Koch6 { ; Adrian Mariano axiom f+f+f+f f=f-ff+ff+f+f-f-ff+f+f-f-ff-ff+f angle 4 } Dragon { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 8 Axiom FX F= y=+FX--FY+ x=-FX++FY- } Peano1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 4 Axiom F-F-F-F F=F-F+F+F+F-F-F-F+F } Cesaro { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 34 Axiom FX F= X=----F!X!++++++++F!X!---- } DoubleCesaro { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 4 axiom D\90D\90D\90D\90 D=\42!D!/84!D!\42 } FlowSnake { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle=6; axiom FL L=FL-FR--FR+FL++FLFL+FR-", R=+FL-FRFR--FR-FL++FL+FR", F= } CantorDust { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 6 Axiom F F=FGF G=GGG } Snowflake2 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 12 axiom F F=++!F!F--F--F@IQ3|+F!F-- F=F--F!+++@Q3F@QI3|+F!F@Q3|+F!F } SnowflakeColor { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 12 axiom F F=--!F<1!F<1++F<1++F<1@IQ3|-F<1!F<1++ F=F<1++F<1!---@Q3F<1@QI3|-F<1!F<1@Q3|-F<1!F<1 F= } Island1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 4 axiom F+F+F+F F=FFFF-F+F+F-F[-GFF+F+FF+F]FF G=@8G@I8 } Island2 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 4 axiom f+f+f+f f=f+gf-ff-f-ff+g+ff-gf+ff+f+ff-g-fff g=@6G@I6 } Quartet { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 4 axiom fb A=FBFA+HFA+FB-FA B=FB+FA-FB-JFBFA F= H=- J=+ } SnowFlake1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 12 Axiom FR R=++!FRFU++FU++FU!---@Q3FU|-@IQ3!FRFU! U=!FRFU!|+@Q3FR@IQ3+++!FR--FR--FRFU!-- F= } SnowFlake3 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 12 axiom fx x=++f!x!fy--fx--fy|+@iq3fyf!x!++f!y!++f!y!fx@q3+++f!y!fx y=fyf!x!+++@iq3fyf!x!++f!x!++f!y!fx@q3|+fx--fy--fxf!y!++ f= } Tree1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle=12; axiom +++FX X=@.6[-FX]+FX } Peano2 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 8 Axiom FXY++F++FXY++F X=XY@Q2-F@IQ2-FXY++F++FXY Y=-@Q2F-@IQ2FXY } Sierpinski1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 3 axiom F F=FXF X=+FXF-FXF-FXF+ } Koch4 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 12 axiom f++++f++++f f=+f--f++f- } Plant07 { ; Ken Philip, from The Science of Fractal Images p.285b axiom Z z=zFX[+Z][-Z] x=x[-FFF][+FFF]FX angle 14 } Plant08 { ; Ken Philip, from The Science of Fractal Images, p.286 axiom SLFFF s=[+++Z][---Z]TS z=+H[-Z]L h=-Z[+H]L t=TL l=[-FFF][+FFF]F angle 20 } Hilbert { ; Ken Philip, from The Science of Fractal Images axiom x x=-YF+XFX+FY- y=+XF-YFY-FX+ angle 4 } Sierpinski3 { ; From Jim Hanan via Corbit axiom F-F-F f=F[-F]F angle 3 } Peano3 { axiom x x=XFYFX+F+YFXFY-F-XFYFX y=YFXFY-F-XFYFX+F+YFXFY angle 4 } Koch5 { axiom f+F+F+F f=F+F-F-FFF+F+F-F angle 4 } Sierpinski2 { ; from The Science of Fractal Images axiom FXF--FF--FF f=FF x=--FXF++FXF++FXF-- angle 6 } SierpinskiSquare { axiom F+F+F+F f=FF+F+F+F+FF angle 4 } Pentagram { ; created by Adrian Mariano angle 10 axiom fx++fx++fx++fx++fx ; f=f[++++@1.618033989f] x=[++++@i1.618033989f@.618033989f!x!@i.618033989f] } QuadKoch { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Quadratic Koch island, Figure 1.7a p.9 angle 4 AXIOM F-F-F-F- F=F+FF-FF-F-F+F+FF-F-F+F+FF+FF-F } Fass1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; FASS curve (3x3 tiles form macrotile), Figure 1.16a p.17 axiom -l angle 4 L=LF+RFR+FL-F-LFLFL-FRFR+ R=-LFLF+RFRFR+F+RF-LFL-FR } Fass2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; FASS curve (4x4 tiles form macrotile), Figure 1.16b p.17 angle 4 axiom -l L=LFLF+RFR+FLFL-FRF-LFL-FR+F+RF-LFL-FRFRFR+ R=-LFLFLF+RFR+FL-F-LF+RFR+FLF+RFRF-LFL-FRFR } QuadGosper { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Quadratic Gosper curve, Figure 1.11b p.12 angle 4 axiom -Fr l=FlFl-Fr-Fr+Fl+Fl-Fr-FrFl+Fr+FlFlFr-Fl+Fr+FlFl+Fr-FlFr-Fr-Fl+Fl+FrFr- r=+FlFl-Fr-Fr+Fl+FlFr+Fl-FrFr-Fl-Fr+FlFrFr-Fl-FrFl+Fl+Fr-Fr-Fl+Fl+FrFr f= } Plant01 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24a p.25 ; also p.285a The Science of Fractal Images angle 14 axiom f f=F[+F]F[-F]F } Plant02 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24b p.25 angle 18 axiom f f=F[+F]F[-F][F] } Plant03 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24c p.25 angle 16 axiom f f=FF-[-F+F+F]+[+F-F-F] } Plant04 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24d p.25 angle 18 axiom x X=F[+X]F[-X]+X F=FF } Plant05 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24e p.25 angle 14 axiom x X=f[+X][-X]FX F=FF } Plant06 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Plant-like structure, figure 1.24f p.25 angle 16 axiom x X=F-[[X]+X]+F[+FX]-X F=FF } Plant09 { ; Adrian Mariano axiom y x=X[-FFF][+FFF]FX y=YFX[+Y][-Y] angle 14 } Plant10 { ; Adrian Mariano axiom f f=f[+ff][-ff]f[+ff][-ff]f angle 10 } Plant11 { ; Adrian Mariano axiom f f=F[+F[+F][-F]F][-F[+F][-F]F]F[+F][-F]F angle 12 } Curve1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; curve from figure 1.9a p.10 angle 4 axiom F-F-F-F- f=FF-F-F-F-F-F+F } Curve2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants angle 4 axiom F-F-F-F- f=FF-F+F-F-FF } Curve3 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; curve from figure 1.9e p.10 axiom F-F-F-F- angle 4 F=F-FF--F-F } Curve4 { ; Adrian Mariano axiom yf x=YF+XF+Y y=XF-YF-X angle 6 } Leaf1 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Compound leaf with alternating branches, Figure 5.12b p.130 angle 8 axiom x a=n n=o o=p p=x b=e e=h h=j j=y x=F[+A(4)]Fy y=F[-B(4)]Fx F=@1.18F@i1.18 } Leaf2 { ; Adrian Mariano, from the Algorithmic Beauty of Plants ; Compound leaf with alternating branches, Figure 5.12a p.130 angle 8 axiom a a=f[+x]fb b=f[-y]fa x=a y=b f=@1.36f@i1.36 } Bush { ; Adrian Mariano Angle 16 Axiom ++++F F=FF-[-F+F+F]+[+F-F-F] } MyTree { ; Adrian Mariano Angle 16 Axiom ++++F F=FF-[XY]+[XY] X=+FY Y=-FX } ColorTriangGasket { ; Adrian Mariano Angle 6 Axiom --X X=++FXF++FXF++FXF>1 F=FF } SquareGasket { ; Adrian Mariano Angle 4 Axiom X X=+FXF+FXF+FXF+FXF F=FF } DragonCurve { ; Adrian Mariano Angle 4 Axiom X X=X-YF- Y=+FX+Y } Square { ; Adrian Mariano Angle 4 Axiom F+F+F+F F=FF+F+F+F+FF } KochCurve { ; Adrian Mariano Angle 6 Axiom F F=F+F--F+F } Penrose1 { ; by Herb Savage ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", ; Roger Penrose's rhombuses Angle 10 Axiom +WF--XF---YF--ZF W=YF++ZF----XF[-YF----WF]++ X=+YF--ZF[---WF--XF]+ Y=-WF++XF[+++YF++ZF]- Z=--YF++++WF[+ZF++++XF]--XF F= } ColorPenrose1 { ; 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 Angle 10 Axiom +WC02F--XC04F---YC04F--ZC02F W=YC04F++ZC02F----XC04F[-YC04F----WC02F]++ X=+YC04F--ZC02F[---WC02F--XC04F]+ Y=-WC02F++XC04F[+++YC04F++ZC02F]- Z=--YC04F++++WC02F[+ZC02F++++XC04F]--XC04F F= } Penrose2 { ; by Herb Savage ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", ; Roger Penrose's rhombuses Angle 10 Axiom ++ZF----XF-YF----WF W=YF++ZF----XF[-YF----WF]++ X=+YF--ZF[---WF--XF]+ Y=-WF++XF[+++YF++ZF]- Z=--YF++++WF[+ZF++++XF]--XF F= } Penrose3 { ; by Herb Savage ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", ; Roger Penrose's rhombuses Angle 10 Axiom [X]++[X]++[X]++[X]++[X] W=YF++ZF----XF[-YF----WF]++ X=+YF--ZF[---WF--XF]+ Y=-WF++XF[+++YF++ZF]- Z=--YF++++WF[+ZF++++XF]--XF F= } Penrose4 { ; by Herb Savage ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", ; Roger Penrose's rhombuses Angle 10 Axiom [Y]++[Y]++[Y]++[Y]++[Y] W=YF++ZF----XF[-YF----WF]++ X=+YF--ZF[---WF--XF]+ Y=-WF++XF[+++YF++ZF]- Z=--YF++++WF[+ZF++++XF]--XF F= } DoublePenrose { ; by Herb Savage ; This is Penrose3 and Penrose4 superimposed Angle 10 Axiom [X][Y]++[X][Y]++[X][Y]++[X][Y]++[X][Y] W=YF++ZF----XF[-YF----WF]++ X=+YF--ZF[---WF--XF]+ Y=-WF++XF[+++YF++ZF]- Z=--YF++++WF[+ZF++++XF]--XF F= } Sphinx { ; by Herb Savage ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers" ; This is an example of a "reptile" Angle 6 Axiom X X=+FF-YFF+FF--FFF|X|F--YFFFYFFF| Y=-FF+XFF-FF++FFF|Y|F++XFFFXFFF| F=GG G=GG } PentaPlexity { ; 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. Angle 10 Axiom F++F++F++F++F 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 CircularTile { ; Adrian Mariano axiom X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X+X x=[F+F+F+F[---X-Y]+++++F++++++++F-F-F-F] y=[F+F+F+F[---Y]+++++F++++++++F-F-F-F] angle 24 }