An exhibition of one approach to interpolating between successive iterations of an L-system. Others are certainly possible (and, as illustrated by SquareTiling, desirable.) Morgan L. Owens "These are rather jerky, unilluminating animations [of iterations of the Hilbert curve] since the process is discrete - there are no possible intermediate frames." KochCurve{ Angle 6 Axiom f f=f-f++f-f } HeighwayDragon{ Angle 4 Axiom xf f= x=xf+yf y=xf-yf } SquareTiling { Angle 4 Axiom s s=sfsf+fsf+fsf+ff+ f=gg g=gg } Pentigree {;William McWorter's Pentigree Angle 10 Axiom f f=-f--f|-f++f--f--f+ } Sierpinskicarpet{ Angle 4 Axiom f f=f[-f+f+f]+f-f-f+f } Hilbert { ; Ken Philip, from The Science of Fractal Images axiom x x=-YF+XFX+FY- y=+XF-YFY-FX+ angle 4 } Peano1 { Angle 4 Axiom f-f-f-f f=f-f+f+f+f-f-f-f+f } Peano3 { axiom x x=XFYFX+F+YFXFY-F-XFYFX y=YFXFY-F-XFYFX+F+YFXFY angle 4 } Sierpinski1 { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot angle 3 axiom F F=FXF X=+FXF-FXF-FXF+ } Curve4 { ; Adrian Mariano axiom yf x=YF+XF+Y y=XF-YF-X angle 6 } KochCurve10{ Angle 6 Axiom d l=/50 r=\50 d=d/10ld\10\10rrd/10ld } KochCurve15{ Angle 6 Axiom d l=/45 r=\45 d=d/15ld\15\15rrd/15ld } KochCurve20{ Angle 6 Axiom d l=/40 r=\40 d=d/20ld\20\20rrd/20ld } KochCurve30{ Angle 6 Axiom d l=/30 r=\30 d=d/30ld\30\30rrd/30ld } KochCurve45{ Angle 6 Axiom d l=/15 r=\15 d=d/45ld\45\45rrd/45ld } KochCurve60{ Angle 6 Axiom d l= r= d=d/60ld\60\60rrd/60ld } HeighwayDragon10{ Angle 4 Axiom xd d= l=/80 r=\80 x=xd\10ryd y=xd/10lyd } HeighwayDragon30{ Angle 4 Axiom xd d= l=/60 r=\60 x=xd\30ryd y=xd/30lyd } HeighwayDragon45{ Angle 4 Axiom xd d= l=/45 r=\45 x=xd\45ryd y=xd/45lyd } HeighwayDragon60{ Angle 4 Axiom xd d= l=/30 r=\30 x=xd\60ryd y=xd/60lyd } HeighwayDragon80{ Angle 4 Axiom xd d= l=/10 r=\10 x=xd\80ryd y=xd/80lyd } HeighwayDragon90{ Angle 4 Axiom xd d= l= r= x=xd\90ryd y=xd/90lyd } SquareTiling10 { Angle 4 Axiom s r=\80 s=sdsd\10rdsd\10rdsd\10rdd\10r d=mm m=mm } SquareTiling30 { Angle 4 Axiom s r=\60 s=sdsd\30rdsd\30rdsd\30rdd\30r d=mm m=mm } SquareTiling45 { Angle 4 Axiom s r=\45 s=sdsd\45rdsd\45rdsd\45rdd\45r d=mm m=mm } SquareTiling60 { Angle 4 Axiom s r=\30 s=sdsd\60rdsd\60rdsd\60rdd\60r d=mm m=mm } SquareTiling80 { Angle 4 Axiom s r=\10 s=sdsd\80rdsd\80rdsd\80rdd\80r d=mm m=mm } SquareTiling81 { Angle 4 Axiom s r=/81\90 s=sdsd\81rdsd\81rdsd\81rdd\81r d=mm m=mm } SquareTiling82 { Angle 4 Axiom s r=/82\90 s=sdsd\82rdsd\82rdsd\82rdd\82r d=mm m=mm } SquareTiling83 { Angle 4 Axiom s r=/83\90 s=sdsd\83rdsd\83rdsd\83rdd\83r d=mm m=mm } SquareTiling84 { Angle 4 Axiom s r=/84\90 s=sdsd\84rdsd\84rdsd\84rdd\84r d=mm m=mm } SquareTiling85 { Angle 4 Axiom s r=/85\90 s=sdsd\85rdsd\85rdsd\85rdd\85r d=mm m=mm } SquareTiling86 { Angle 4 Axiom s r=/86\90 s=sdsd\86rdsd\86rdsd\86rdd\86r d=mm m=mm } SquareTiling87 { Angle 4 Axiom s r=/87\90 s=sdsd\87rdsd\87rdsd\87rdd\87r d=mm m=mm } SquareTiling88 { Angle 4 Axiom s r=/88\90 s=sdsd\88rdsd\88rdsd\88rdd\88r d=mm m=mm } SquareTiling89 { Angle 4 Axiom s r=\1 s=sdsd\89rdsd\89rdsd\89rdd\89r d=mm m=mm } SquareTiling90 { Angle 4 Axiom s r=/90\90 s=sdsd\90rdsd\90rdsd\90rdd\90r d=mm m=mm } Pentigree10 { Angle 10 Axiom d l=/26 r=\26 d=/10ld/10l/10ld\10r\10r\10r\10rd\10r\10rd/10l/10ld/10l/10ld\10r } Pentigree15 { Angle 10 Axiom d l=/21 r=\21 d=/15ld/15l/15ld\15r\15r\15r\15rd\15r\15rd/15l/15ld/15l/15ld\15r } Pentigree20 { Angle 10 Axiom d l=/16 r=\16 d=/20ld/20l/20ld\20r\20r\20r\20rd\20r\20rd/20l/20ld/20l/20ld\20r } Pentigree30 { Angle 10 Axiom d l=/6 r=\6 d=/30ld/30l/30ld\30r\30r\30r\30rd\30r\30rd/30l/30ld/30l/30ld\30r } Pentigree36 { Angle 10 Axiom d l= r= d=/36ld/36l/36ld\36r\36r\36r\36rd\36r\36rd/36l/36ld/36l/36ld\36r } Sierpinskicarpet10{ Angle 4 Axiom d l=/80 r=\80 d=d[/10ld\10rd\10rd]\10rd/10ld/10ld\10rd } Sierpinskicarpet15{ Angle 4 Axiom d l=/75 r=\75 d=d[/15ld\15rd\15rd]\15rd/15ld/15ld\15rd } Sierpinskicarpet30{ Angle 4 Axiom d l=/60 r=\60 d=d[/30ld\30rd\30rd]\30rd/30ld/30ld\30rd } Sierpinskicarpet45{ Angle 4 Axiom d l=/45 r=\45 d=d[/45ld\45rd\45rd]\45rd/45ld/45ld\45rd } Sierpinskicarpet60{ Angle 4 Axiom d l=/30 r=\30 d=d[/60ld\60rd\60rd]\60rd/60ld/60ld\60rd } Sierpinskicarpet80{ Angle 4 Axiom d l=/10 r=\10 d=d[/80ld\80rd\80rd]\80rd/80ld/80ld\80rd } Sierpinskicarpet90{ Angle 4 Axiom d l= r= d=d[/90ld\90rd\90rd]\90rd/90ld/90ld\90rd } Hilbert1 { axiom x l=\89 r=/89 x=/1lYd\1rXdX\1rdY/1l y=\1rXd/1lYdY/1ldX\1r angle 4 } Hilbert10 { axiom x l=\80 r=/80 x=/10lYd\10rXdX\10rdY/10l y=\10rXd/10lYdY/10ldX\10r angle 4 } Hilbert15 { axiom x l=\75 r=/75 x=/15lYd\15rXdX\15rdY/15l y=\15rXd/15lYdY/15ldX\15r angle 4 } Hilbert30 { axiom x l=\60 r=/60 x=/30lYd\30rXdX\30rdY/30l y=\30rXd/30lYdY/30ldX\30r angle 4 } Hilbert45 { axiom x l=\45 r=/45 x=/45lYd\45rXdX\45rdY/45l y=\45rXd/45lYdY/45ldX\45r angle 4 } Hilbert60 { axiom x l=\30 r=/30 x=/60lYd\60rXdX\60rdY/60l y=\60rXd/60lYdY/60ldX\60r angle 4 } Hilbert80 { axiom x l=\10 r=/10 x=/80lYd\80rXdX\80rdY/80l y=\80rXd/80lYdY/80ldX\80r angle 4 } Hilbert89 { axiom x l=\1 r=/1 x=/89lYd\89rXdX\89rdY/89l y=\89rXd/89lYdY/89ldX\89r angle 4 } Hilbert90 { axiom x l= r= x=/90lYd\90rXdX\90rdY/90l y=\90rXd/90lYdY/90ldX\90r angle 4 } Peano1-1 { Angle 4 Axiom d/90d/90d/90d l=/89 r=\89 d=d/1ld\1rd\1rd\1rd/1ld/1ld/1ld\1rd } Peano1-10 { Angle 4 Axiom d/90d/90d/90d l=/80 r=\80 d=d/10ld\10rd\10rd\10rd/10ld/10ld/10ld\10rd } Peano1-45 { Angle 4 Axiom d/90d/90d/90d l=/45 r=\45 d=d/45ld\45rd\45rd\45rd/45ld/45ld/45ld\45rd } Peano1-60 { Angle 4 Axiom d/90d/90d/90d l=/30 r=\30 d=d/60ld\60rd\60rd\60rd/60ld/60ld/60ld\60rd } Peano1-80 { Angle 4 Axiom d/90d/90d/90d l=/10 r=\10 d=d/80ld\80rd\80rd\80rd/80ld/80ld/80ld\80rd } Peano1-89 { Angle 4 l=/1 r=\1 Axiom d/90d/90d/90d d=d/89ld\89rd\89rd\89rd/89ld/89ld/89ld\89rd }