Alien { ; William McWorter Angle 11 Axiom x x=[@q2@I2-fx]g[@q2@I2---fx] f= } AmmannPoly { ;; by Philippe Hurbain ;; Same as AmmanPolyColor, showing only the ;; pentagon/hexagon tiling Angle 10 Axiom x x=@.618034/36[\9@.66D]M[/196.5@.363D][/180y]\72M[/180x] x=[\144@.618034M@i.618034x]\108[\36@.509D@1.18\30D][x]M[\153@.66D]\72[y]M y=@.618034/72[x][\36@.509D]M\144[\9@.66D]M[/180y][/196.5@.363D] y=\36[y]M\144M[/180x] D=M } Border1 { ; William McWorter Angle 4 Axiom XYXYXYX+XYXYXYX+XYXYXYX+XYXYXYX F= X=FX+FX+FXFY-FY- Y=+FX+FXFY-FY-FY } Boundary { ; William McWorter ; Dekking's boundary of the Twindragon Angle 4 Axiom otuz f= o=fo+f-t p=++f--u+f-x q=-f+v++f--q r=-f+zfs s=fw t=++f--u u=++f--y v=fs w=fo+f-p x=++f--y+f-x y=-f+r++f--q z=-f+zfw } Bush { ; Adrian Mariano Angle 16 Axiom ++++F F=FF-[-F+F+F]+[+F-F-F] } Cross { ; William McWorter Angle 4 Axiom FX F= X=FX+FX+FXFY-FY- Y=+FX+FXFY-FY-FY } Dekking { ; Dekking's Church ; Advances in Math, Vol. 44, 1982, pp.78-104 Angle 4 Axiom C32WC06ZC15YC06X F= W=FW+F-XFW-F+Z X=++F--Y-F+Z++F--Y-F+Z Y=++F--Y+F-X Z=FW+F-X } Dekking1 { Angle 3 Axiom x+x+x x=fy+gx-fy y=gx+fy-gx f= g= } Doublecrossmed { ; William McWorter Angle 8 Axiom +x x=x-f-y-f-x+f+y+f+x+f+y-f-x-f-y y=x+f+y+f+x-f-y-f-x-f-y+f+x+f+y } Doily { ; Adrian Mariano Angle 12 Axiom f--f--f--f--f--f f=-f[--f--f]++f--f+ } Doily-c { Angle 12 Axiom c32f--c36f--c40f--c44f--c48f--c52f ; from Default.map f=-f[--f--f]++f--f+ } Doily1 { Angle 12 Axiom f--f--f--f--f--f f=-f[--f--f]++f[++f--f]--f+ } Dragon { ; Adrian Mariano ; from The Fractal Geometry of Nature by Mandelbrot Angle 8 Axiom FX F= y=+FX--FY+ x=-FX++FY- } Dragon-wm { ; William McWorter Angle 4 Axiom X F= X=FX+FY ; Do first half, turn left 90 degrees, do second half Y=FX-FY ; Trace first half (X) backwards; Y backwards is X, ; left turn becomes right turn, and X backwards is Y } Dragon1 { ; William McWorter Angle 8 Axiom X F= X=FX+@.500FZ@2.00+FY Y=FX-@.500FZ@2.00-FY Z=FZ } DragonAlt { ; William McWorter Angle 8 Axiom -c32X+[+++@.5gw---c40@q2fz]+c48y F= g= X=fx+[+++@.5gw---c40@q2fz]+fy Y=Fx-[---@.5gw+++c40@q2fz]-fy z=fz w=gw } DragonAlt1 { ; William McWorter Angle 8 Axiom X F= X=FX+@.500FZ@2.00+FY Y=FX-@.500FZ@2.00-FY Z=FZ } DragonCurd { ; William McWorter Angle 4 Axiom su f= g= s=fs+g-x t=++f--u+g-x u=++f--u-g+z v=fs-g+z w=gw+f-t x=++g--y+f-t y=++g--y-f+v z=gw-f+v } Dragonrnd { ; William McWorter Angle 8 Axiom X F= X=FX+@.500FZ@2.00+FY Y=FX-@.500FZ@2.00-FY Z=FZ } Dragon&med { ; William McWorter Angle 8 Axiom -c32X+[+++@.5gw---c40@q2fz]+c48y F= g= X=fx+[+++@.5gw---c40@q2fz]+fy Y=Fx-[---@.5gw+++c40@q2fz]-fy z=fz w=gw } 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 } FracRhombusTile { ; William McWorter Angle 12 Axiom f f=[-f++g-]+f--g+ g=[-f++g-]+f--g+ } Frame { ; William McWorter ; made from Moore's spacefilling curve Angle 4 Axiom YXY-YXY-YXY-YXY F= X=FX+FX+FXFYFX+FXFY-FY-FY- Y=+FX+FX+FXFY-FYFXFY-FY-FY } Grid { Angle 4 ; Allow turns of 90=360/4 degrees Axiom f ; Birth string is the symbol f (see text below) f=f[+f][-f]f ; Replacement string for f (see text below) } Grid1 { ; William McWorter Angle 4 Axiom x x=y y=f f=f[+f][-f]f } GridMedian { ; William McWorter Angle 4 Axiom z z=x x=-[c40@I2g+f+@2f+f+f+@I2f]yfw+[c40@I2g+f+@2f+f+f+@I2f]xfw x=[c40@I2g+f+@2f+f+f+@I2f]x+fw[c40@I2g+f+@2f+f+f+@I2f]y- y=+[c40@I2g+f+@2f+f+f+@I2f]xfw-[c40@I2g+f+@2f+f+f+@I2f]yfw y=[c40@I2g+f+@2f+f+f+@I2f]y-fw[c40@I2g+f+@2f+f+f+@I2f]x+ w=fw f= g= } Hex { Angle 6 ; Turns are 60=360/6 degrees Axiom f ; Birth string is f f=-f+f+g[+f+f]- ; Replacement string for f g=gg ; Replacement string for g (see text below) } Hex1 { Angle 6 Axiom f f=-f+f+f[+f+f+f]- } Hilbert { ; Ken Philip, from The Science of Fractal Images axiom x x=-YF+XFX+FY- ; cup interior on left during trace y=+XF-YFY-FX+ ; cup interior on right during trace angle 4 } Hilbert1 { axiom z z=-c32Yc15f+c32Xc15Fc32X+c15Fc32Y- x=-YF+XFX+FY- y=+XF-YFY-FX+ angle 4 } Hiway { Angle 4 Axiom fx x=fx+fy y=fx-fy f= } Hiway1 { Angle 8 Axiom u F= g= u=v v=c32fX+[+++@.5gw---c40@q2fz]+c48fy X=fx+[+++@.5gw---c40@q2fz]+fy Y=Fx-[---@.5gw+++c40@q2fz]-fy z=fz w=gw } Hiwayint { ; William McWorter Angle 4 Axiom s F= s=x+F-t t=++F--u+F-t u=z-F+v v=Fs-F+v w=Fsw x=xy y=++F--uy z=zw } Hiwaymed { Angle 8 ; Smallest turn is 45=360/8 degrees Axiom -X ; Turn whole thing 45 degrees so that all lines of X are horizontal or vertical X=X+F+Y ; Do X, turn left, forward, turn left, do Y Y=X-F-Y ; Do X backwards } Hiwaymed-x { ; William McWorter Angle 4 Axiom s F= s=Fs+F-t t=+F-u+F-t u=++F--v++F--w v=++F--v-F+x w=-F+y++F--w x=-F+y-F+x y=FsFz z=+F-uFz } Isocepent { ; William McWorter Angle 10 Axiom w w=++[-@1.618033989f@I1.618033989++++f]fx--[++@1.618033989f----f]fw-- w=[--@1.618033989f++++f]fy++ x=-[+@1.618033989f@I1.618033989----f]fz++[--@1.618033989f++++f]fy- y=--[+@1.618033989f@I1.6180339898----f]fz++[--@1.618033989f++++f]fy++ y=[++@1.618033989f----f]fw-- z=+[-@1.618033989f@I1.618033989++++f]fx--[++@1.618033989f----f]fw+ f= } Isocepent-1 { ; William McWorter Angle 10 Axiom s s=w w=++[-@1.618033989f@I1.618033989++++f]fx--[++@1.618033989f----f]fw-- w=[--@1.618033989f++++f]fy++ x=-[+@1.618033989f@I1.618033989----f]fz++[--@1.618033989f++++f]fy- y=--[+@1.618033989f@I1.6180339898----f]fz++[--@1.618033989f++++f]fy++ y=[++@1.618033989f----f]fw-- z=+[-@1.618033989f@I1.618033989++++f]fx--[++@1.618033989f----f]fw+ f= } Isocepent-2 { ; William McWorter Angle 10 Axiom s s=z w=++[-@1.618033989f@I1.618033989++++f]fx--[++@1.618033989f----f]fw-- w=[--@1.618033989f++++f]fy++ x=-[+@1.618033989f@I1.618033989----f]fz++[--@1.618033989f++++f]fy- y=--[+@1.618033989f@I1.6180339898----f]fz++[--@1.618033989f++++f]fy++ y=[++@1.618033989f----f]fw-- z=+[-@1.618033989f@I1.618033989++++f]fx--[++@1.618033989f----f]fw+ f= } isocright { Angle 8 Axiom x x=+y-f-y+ y=-x+f+x- } KochCurve { ; Adrian Mariano Angle 6 Axiom F F=F+F--F+F } Lace { ; William McWorter ; A 30-60-90 triangle dissects into three ; congruent 30-60-90 triangles ; This script traverses the centers of the congruent triangles Angle 12 Axiom w w=+++x--F--zFx+ x=---w++F++yFw- y=+zFx--F--z+++ z=-yFw++F++y--- } 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 } Leafy { Angle 50 Axiom +++++++++++++c6x x=f[@.5+++++++++x@.5f+++++++c48f--f|++++f------f] x=-f[@.4-----------!x@.5f+++++++c48f--f|++++f------f] x=@.6x } LawnInSpring { Angle 16 Axiom c49x x=[+++++f-f-fz]gx++++gy y=[+++++f-f-fz]gx----gy z=w w=u u=[c44@.3[+++f]g++[+++f]g++[+++f]g++[+++f]g++[+++f]g++[+++f]g++[+++f]g++[+++f]g]z f= g= } Maze01 { Angle 3 Axiom c40f+c48f+c56f f=f+ff-f } Maze&Fractal1 { Angle 3 Axiom x x=fy+fyfy-fy y=fx-fxfx+fx f= } Moore { ; William McWorter Angle 4 Axiom X F= X=FX+FX+FXFYFX+FXFY-FY-FY- Y=+FX+FX+FXFY-FYFXFY-FY-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 } Peanomed { ; William McWorter Angle 8 Axiom -X X=X+F+X-F-X-F-X-F-X+F+X+F+X+F+X-F-X } Pentant { ; William McWorter Angle 5 Axiom x-x-x-x-x f= x=fx-fx-fx+fy+fy+fx-fx y=fy+fy-fx-fx-fy+fy+fy } PentaPlexity-0 { ; 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 } Pentigree { ; William McWorter Angle 5 Axiom F-F-F-F-F F=F-F++F+F-F-F } Pentive { Angle 10 Axiom W F= W=++FX--FW--FY++ X=-FZ++FY- Y=--FZ++FY++FW-- Z=+FX--FW+ } Pentive1 { Angle 10 Axiom x f= g= x=++fz----fy++fx y=+fw--gz+ z=--fx++++fw--fz w=-fy++gx- } Pentive2 { Angle 10 Axiom x f= x=fy++fz----fw++ y=+fw--fu+ z=++fv----fx++fy w=fu--fv++++fx-- u=-fx++fy- v=--fz++++fw--fu } Pentive3 { Angle 10 Axiom q f= p=--fr++++fs--fu q=ft++fr----fs++ r=++fp----fq++ft s=fu--fp++++fq-- t=+fu--fp+ u=-fq++ft- } Penty { ; William McWorter * Angle 10 Axiom W F= W=++c15FX--c48FW--c48FY++ X=-c15FZ++c40FY- Y=--c15FZ++c40FY++c48FW-- Z=+c15FX--c40FW+ } Pentl { ; William McWorter Angle 5 Axiom f-f-f-f-f f=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 } PreLace { Angle 12 Axiom +++c32fw----c15fzc48fw+ f= y=+++fw----fzfw+ x=+fzfw----fz+++ w=---fy++++fxfy- z=-fxfy++++fx--- } RhombusTile { Angle 12 Axiom f f=[-f++f-]+f--f+ } Sierpinsk { ; William McWorter ; Isoceles right triangle dissects into two congruent ; isoceles right triangles Angle 8 Axiom L L=+R-F-R+ R=-L+F+L- } Sierpinski { ; William McWorter Angle 8 Axiom L--F--L--F L=+R-F-R+ R=-L+F+L- } Sierpinski1 { Angle 8 Axiom z z=x x=+[c40-@.5g++@2.414g|@q2f--f---@q2f]y-fw- x=[c40-@.5g++@2.414g|@q2f--f---@q2f]y+ y=-[c40+@.5g--@2.414g|@q2f++f+++@q2f]x+fw+ y=[c40+@.5g--@2.414g|@q2f++f+++@q2f]x- w=fw f= g= } SierpinskiCarpet { Angle 4 Axiom f f=f+f-f-f-g+f+f+f-f g=ggg } Snowflake { Angle 6 ; All turns are multiples of 60=360/6 degrees Axiom f--f--f ; Draw clockwise a ring of three Snowflakes f=f+f--f+f ; Forward, turn left, forward, turn left, turn left, ... , forward } 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 } SquareGasket { ; Adrian Mariano Angle 4 Axiom x x=+fxf+fxf+fxf+fxf f=ff } Stars&Pentas2 { ;; by Philippe Hurbain ;; Penrose's stars and pentagons, generated from ;; decomposition rules ;; u is the star, v is the boat, w is the thin rhombus ;; x, y and z are the pentagons Angle 10 Axiom u u=@.381966[v]F[|y][-u]++F|+[v]F[|y]++F|+[v]F[|y]++F|+ u=[v]F[|y]++F|+[v]F[|y]++F v=@.381966[v]F[|y]++F|+[v]F[|y]-[u]F-F|+[v]F[|y]++F w=@.381966G++[u]F|+F-F|+[v]F[|y] y=@.381966[x][y][w]F[|!y]++F++[y][w]F[|!y]++F++[z]F x=@.381966G++G++[!x][!z]F--[!z]F--[!z]F--[!z]F--[!z]F z=@.381966[z][x]F++[z]F++[w][y]F[|!y]++F++[z]F F=G } Strike_S { ; William McWorter ; Strikethrough S Angle 4 Axiom UW F= U=FU+F-V V=++F--W++F--Z W=++F--W-F+X X=FUFY Y=+F-VFY Z=-F+X--F++Z } Terdragon { ; William McWorter ; from Davis and Knuth. Journal of ; Rec. Math. vol. 3, 1970, pages 61-81 Angle 3 Axiom F F=F+F-F } Terdragon-c { ; William McWorter ; from Davis and Knuth. Journal of ; Rec. Math. vol. 3, 1970, pages 61-81 Angle 3 Axiom c15F+c48F-c40F F=F+F-F } Terdragon1 { Angle 3 Axiom x x=y y=c15F+c48F-c40F F=F+F-F } TerdragnM { ; William McWorter ; median terdragon Angle 6 Axiom X X=X+F+X-F-X } ThreeTile { Angle 12 Axiom [c32u]@q3" "=u u=[+++@iq3f----@2f]fx x=+++[---@iq3f++++@2f]fy----[-@2@iq3f++++@i2f]fz[---@iq3f++++@2f]fy+ y=---[+++@iq3f----@2f]fx++++[+@2@iq3f----@i2f]fw[+++@iq3f----@2f]fx- z=-[+@2@iq3f----@i2f]fw[+++@iq3f----@2f]fx++++[+@2@iq3f----@i2f]fw--- w=+[-@2@iq3f++++@i2f]fz[---@iq3f++++@2f]fy----[-@2@iq3f++++@i2f]fz+++ f= } ThreeTile&med { Angle 12 Axiom u u=[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x x=+++[c32----g-----@1.366f---@q3f-----@2@iq3f]y--fp-- x=[c32--g+++++@1.366f+++@q3f+++++@2@iq3f]zfp x=[c32----g-----@1.366f---@q3f-----@2@iq3f]y+ y=---[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x++fp++ y=[c32++g-----@1.366f---@q3f-----@2@iq3f]wfp y=[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x- z=-[c32++g-----@1.366f---@q3f-----@2@iq3f]wfp z=[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x++fp++ z=[c32++g-----@1.366f---@q3f-----@2@iq3f]w--- w=+[c32--g+++++@1.366f+++@q3f+++++@2@iq3f]zfp w=[c32----g-----@1.366f---@q3f-----@2@iq3f]y--fp-- w=[c32--g+++++@1.366f+++@q3f+++++@2@iq3f]z+++ p=fp f= g= } ThreeTile&med1 { Angle 12 Axiom u---fp---v---fp v=[c32++g-----@1.366f---@q3f-----@2@iq3f]w u=[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x x=+++[c32----g-----@1.366f---@q3f-----@2@iq3f]y--fp-- x=[c32--g+++++@1.366f+++@q3f+++++@2@iq3f]zfp x=[c32----g-----@1.366f---@q3f-----@2@iq3f]y+ y=---[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x++fp++ y=[c32++g-----@1.366f---@q3f-----@2@iq3f]wfp y=[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x- z=-[c32++g-----@1.366f---@q3f-----@2@iq3f]wfp z=[c32++++g+++++@1.366f+++@q3f+++++@2@iq3f]x++fp++ z=[c32++g-----@1.366f---@q3f-----@2@iq3f]w--- w=+[c32--g+++++@1.366f+++@q3f+++++@2@iq3f]zfp w=[c32----g-----@1.366f---@q3f-----@2@iq3f]y--fp-- w=[c32--g+++++@1.366f+++@q3f+++++@2@iq3f]z+++ p=fp f= g= } Tiling1 { Angle 6 Axiom x x=f-f-f+f+fx++f-f-f+f+fx--f-f-f+f+fx f= } Trigrid { Angle 3 Axiom f f=f+f-f-ff+f+f-f } Trigrid1 { Angle 6 Axiom x x=fy[+fy][--fy]fy y=fx[++fx][-fx]fx f= } Tripeanomed { ; William McWorter Angle 6 Axiom x x=x+f+x-f-x-f-x+f+x+f+x-f-x } TriPeano { ; William McWorter Angle 3 Axiom f f=f+f-f-f+f+f-f } TwinDragonCurd1 { Angle 4 Axiom fx+c32fx x=fx+gy y=fx-gy f= g= } TwinDragonCurd { Angle 4 Axiom fx+fx x=fx+gy y=gx-fy f= g= } TwoTile { Angle 8 Axiom [c32z]@q2a a=z z=[+@q2@i2f--f]fx x=+[-@q2@i2f++f]fy--[-@q2@i2f++f]fy+ y=-[+@q2@i2f--f]fx++[+@q2@i2f--f]fx- f= } Untitled { ; William McWorter Angle 4 Axiom x f= x=fx-fy-fx+fy+fx+fy-fx-fy+ y=-fx+fy+fx-fy-fx-fy+fx+fy } Untitledmed { ; William McWorter Angle 8 Axiom +x x=x-f-y-f-x+f+y+f+x+f+y-f-x-f-y y=x+f+y+f+x-f-y-f-x-f-y+f+x+f+y } Weed-0 { Angle 50 Axiom +++++++++++++x x=f[@.5+++++++++x]-f[@.4-----------!x]x } Weed { Angle 50 Axiom +++++++++++++x x=f[@.5+++++++++x]-f[@.4-----------!x]@.6x } Vertigo1 { ; by Morgan Savage ; Try order 13 and color cycle in both 256 and 16 color modes Angle 46 Axiom X X=X>1F+@.9997X } VoderbergTile { ; by Herb Savage ; based on Martin Gardner's "Penrose Tiles to Trapdoor Ciphers", ; A spiral tiling by Heinz Voderberg angle 30 axiom \84.1A\96@4.783386117M@I4.783386117/96A A=X\12X\12X\12X\12X\12X\12X\12X\12X\12X\12X\12X\12X\12X\12X\12Z X=[D\78D\46.37236@3.393427D@I3.393427/46.37236D\114[\168X\24Y]D\78D\46.37236@3.393427D@I3.393427/46.37236D/78D] Y=[D\78D\46.37236@3.393427D@I3.393427/46.37236D/78D\168[\192Y]D\78D\46.37236@3.393427D@I3.393427/46.37236D] Z=[D\78D\46.37236@3.393427D@I3.393427/46.37236D\114D\78D\46.37236@3.393427D@I3.393427/46.37236D/78D] } Xmastree { ; William McWorter Angle 10 Axiom p f= p=--<1fr++++<1fs--<1fu q=<1ft++<1fr----<1fs++ r=++<1fp----<1fq++<1ft s=<1fu--<1fp++++<1fq-- t=+<1fu--<1fp+ u=-<1fq++<1ft- } Xmastree-0 { ; William McWorter Angle 10 Axiom W F= W=++c15FX--c48FW--c48FY++ X=-c15FZ++c40FY- Y=--c15FZ++c40FY++c48FW-- Z=+c15FX--c40FW+ }