Category : Printer + Display Graphics
Archive   : FRACT182.ZIP
Filename : PENROSE.L

 
Output of file : PENROSE.L contained in archive : FRACT182.ZIP
{ 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
[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
}



  3 Responses to “Category : Printer + Display Graphics
Archive   : FRACT182.ZIP
Filename : PENROSE.L

  1. Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

  2. This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

  3. But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/