penrose.l

; Generation of Penrose aperiodic tilings

; Thanks to Herb Savage, who showed it was possible to generate those tilings
; with L-systems and Fractint.

; Based on decomposition of tilings described in Tilings and Pattern, by
; Branko Grunbaum and G.C. Shepard, W.H. Freeman and Company, chapter 10

; Philippe Hurbain
; 49 rue Jules Fossier
; 95380 LOUVRES
; FRANCE


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=
}

Losanges {
           ;; by Philippe Hurbain
           ;; Penrose's rhombuses, generated by decomposition rules
           ;; x generate the fat rhombus, y the thin one
           ;; Individualization of rhombuses allows easy coloring
           ;; 0.618034 is ({5-1)/2
  Angle 10
  Axiom x
  x=@.618034+f[|y]--f[|x][|+@.618034g@i.618034x]---[x]f--[y]f
  y=@.618034++[x]f|+f[|y]-[y]f|+f[|x]
  f=g
}

PentaColor {
             ;; by Philippe Hurbain
             ;; Simple coloring of Penrose's rhombuses, showing pentagons
  Angle 20
  Axiom c04[x]++++[x]++++[x]++++[x]++++[x]
  x=@.618034++f[c10@1.1755-------f][|y]----f[|x]
  x=[|++@.618034g@i.618034x]------[x]f----[y]f
  y=@.618034++++[x]f|++f[|y]--[y]f|++f[|x]
  f=g
}

Penta {
        ;; by Philippe Hurbain
        ;; Same as PentaColor, but showing only the coloring
  Angle 20
  Axiom [x]++++[x]++++[x]++++[x]++++[x]
  x=@.618034++g[@1.1755-------f][|y]----g[|x]
  x=[|++@.618034g@i.618034x]------[x]g----[y]g
  y=@.618034++++[x]g|++g[|y]--[y]g|++g[|x]
  f=g
}


Kites&Darts {
              ;; by Philippe Hurbain
              ;; Penrose's kites and darts
              ;; k generates the kite, a generates the dart
  Angle 10
  Axiom k
  k=+[@.618034a]f@.618034---[-k]f-f---[-k]@i.618034f[@.618034|a]
  a=[@.618034k]+f@.618034[|a]----f+f----[a]@i.618034f
  f=g
}

Kites&Darts2 {
               ;; by Philippe Hurbain
               ;; Penrose's kites and darts, with kites seed
  Angle 10
  Axiom [k]++[k]++[k]++[k]++[k]
  k=+[@.618034a]f@.618034---[-k]f-f---[-k]@i.618034f[@.618034|a]
  a=[@.618034k]+f@.618034[|a]----f+f----[a]@i.618034f
  f=g
}

Kites&Darts3 {
               ;; by Philippe Hurbain
               ;; Penrose's kites and darts, with darts seed
  Angle 10
  Axiom [a]++[a]++[a]++[a]++[a]
  k=+[@.618034a]f@.618034---[-k]f-f---[-k]@i.618034f[@.618034|a]
  a=[@.618034k]+f@.618034[|a]----f+f----[a]@i.618034f
  f=g
}

Kites&DartsColor {
                   ;; by Philippe Hurbain
                   ;; Penrose's kites and darts, with serpentine coloring
  Angle 10
  Axiom c4[k]++[k]++[k]++[k]++[k]
  k=+[@.618034a[g---@.618c10f][--g+++@.618c10f]]
  k=f@.618034---[-k]f-f---[-k]@i.618034f[@.618034|a]
  a=[@.618034k]+f@.618034[|a][|g++@.382c10f]----f+
  a=f----[a][g--@.382c10f]@i.618034f
  f=g
}


AmmannPolyColor {  
                  ;; by Philippe Hurbain
                  ;; Ammann's coloring of Penrose's rhombuses, giving an
                  ;; aperiodic tiling of 2 pentagons and 1 hexagon
  Angle 10
  Axiom c1x
  x=@.618034/36[c3\9@.66D]D[c3/196.5@.363D][/180y]\72D[/180x]
  x=[\144@.618034M@i.618034x]\108[c3\36@.509D@1.18\30D][x]D[c3\153@.66D]\72[y]D
  y=@.618034/72[x][c3\36@.509D]D\144[c3\9@.66D]D[/180y][c3/196.5@.363D]
  y=\36[y]D\144D[/180x]
  D=M
}

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
}

Stars&PentasColor {
                ;; by Philippe Hurbain
                ;; Penrose's stars and pentagon tiling, generated as
                ;; a coloring of kites and darts
  Angle 20
  Axiom c04k
  k=++[@.618034[g-c10@.5878[f]------ff++++f]a]f@.618034------
  k=[--k]f--f------[--k]@i.618034f[@.618034|a]
  a=[@.618034k]++f@.618034[|[gc10@.5878+++++++f]a]--------f
  a=++f--------[c10g@.5878-------f][a]@i.618034f
  f=g
}

Stars&Pentas1 {
                ;; by Philippe Hurbain
                ;; Same as Stars&PentasColor, showing only coloring
  Angle 20
  Axiom [k]++++[k]++++[k]++++[k]++++[k]
  k=++[@.618034[g-@.5878[f]------ff++++f]a]g@.618034------
  k=[--k]g--g------[--k]@i.618034g[@.618034|a]
  a=[@.618034k]++g@.618034[|[g@.5878+++++++f]a]--------g
  a=++g--------[g@.5878-------f][a]@i.618034g
  f=g
}


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
}