Category : C Source Code
Archive   : FRASRC18.ZIP
Filename : 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 Grnbaum 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
[email protected]+f[|y]--f[|x][|[email protected]@i.618034x]---[x]f--[y]f
[email protected]++[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]
[email protected]++f[[email protected]][|y]----f[|x]
x=[|[email protected]@i.618034x]------[x]f----[y]f
[email protected]++++[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]
[email protected]++g[@1.1755-------f][|y]----g[|x]
x=[|[email protected]@i.618034x]------[x]g----[y]g
[email protected]++++[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][email protected][-k]f-f---[-k]@i.618034f[@.618034|a]
a=[@.618034k][email protected][|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][email protected][-k]f-f---[-k]@i.618034f[@.618034|a]
a=[@.618034k][email protected][|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][email protected][-k]f-f---[-k]@i.618034f[@.618034|a]
a=[@.618034k][email protected][|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[[email protected]][[email protected]]]
[email protected][-k]f-f---[-k]@i.618034f[@.618034|a]
a=[@.618034k][email protected][|a][|[email protected]]----f+
a=f----[a][[email protected]]@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
[email protected]/36[c3\[email protected]]D[c3/[email protected]][/180y]\72D[/180x]
x=[\[email protected]@i.618034x]\108[c3\[email protected]@1.18\30D][x]D[c3\[email protected]]\72[y]D
[email protected]/72[x][c3\[email protected]]D\144[c3\[email protected]]D[/180y][c3/[email protected]]
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
[email protected]/36[\[email protected]]M[/[email protected]][/180y]\72M[/180x]
x=[\[email protected]@i.618034x]\108[\[email protected]@1.18\30D][x]M[\[email protected]]\72[y]M
[email protected]/72[x][\[email protected]]M\144[\[email protected]]M[/180y][/[email protected]]
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[[email protected][f]------ff++++f]a][email protected]
k=[--k]f--f------[--k]@i.618034f[@.618034|a]
a=[@.618034k][email protected][|[[email protected]+++++++f]a]--------f
a=++f--------[[email protected]][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[[email protected][f]------ff++++f]a][email protected]
k=[--k]g--g------[--k]@i.618034g[@.618034|a]
a=[@.618034k][email protected][|[[email protected]+++++++f]a]--------g
a=++g--------[[email protected]][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
[email protected][v]F[|y][-u]++F|+[v]F[|y]++F|+[v]F[|y]++F|+
u=[v]F[|y]++F|+[v]F[|y]++F
[email protected][v]F[|y]++F|+[v]F[|y]-[u]F-F|+[v]F[|y]++F
[email protected]++[u]F|+F-F|+[v]F[|y]
[email protected][x][y][w]F[|!y]++F++[y][w]F[|!y]++F++[z]F
[email protected]++G++[!x][!z]F--[!z]F--[!z]F--[!z]F--[!z]F
[email protected][z][x]F++[z]F++[w][y]F[|!y]++F++[z]F
F=G
}