Penrose tiling: Difference between revisions

← Older edit

Penrose tiling (view source)

Revision as of 21:52, 13 April 2024

5,584 bytes added , 1 month ago

Added Fōrmulæ entry

Laurence

2,120

edits

Revision as of 01:12, 28 August 2022 (view source) Thundergnat (talk \| contribs) m (syntax highlighting fixup automation) ← Older edit		Latest revision as of 21:52, 13 April 2024 (view source) Laurence (talk \| contribs) (Added Fōrmulæ entry)
(7 intermediate revisions by 5 users not shown)
Line 31: * [http://preshing.com/20110831/penrose-tiling-explained/ Deflation explained for Kite and Dart, includes Python code (preshing.com)] <br><br> =={{header\|11l}}== {{trans\|Python}} <syntaxhighlight lang="11l"> F penrose(depth) print(‘<svg viewBox="-100 -100 200 200" xmlns="http://www.w3.org/2000/svg"> <defs> <path id="A0" d="M 80.90169943749474 58.778525229247315 L 0 0 100 0" stroke="black" fill="#8bc" /> <path id="B0" d="M 0 0 80.90169943749474 58.778525229247315 161.80339887498948 0" stroke="black" fill="#97e" />’) L(d) 0 .< depth print(‘ <g id="A’(d + 1)‘" transform="translate(100, 0) scale(0.6180339887498949)"> <use href="#A’d‘" transform="rotate(108)" /> <use href="#B’d‘" transform="scale(-1, 1)" /> </g> <g id="B’(d + 1)‘"> <use href="#A’(d + 1)‘" /> <use href="#B’d‘" transform="translate(100, 0) scale(0.6180339887498949) rotate(144) translate(-80.90169943749474,-58.778525229247315)"/> </g>’) print(‘ <g id="G"> <use href="#A’depth‘"/> <use href="#A’depth‘" transform="scale(1, -1)" /> </g> </defs> <g transform="scale(2, 2)"> <use href="#G" transform="rotate(-144)" /> <use href="#G" transform="rotate(-72)" /> <use href="#G" transform="rotate(0)" /> <use href="#G" transform="rotate(72)" /> <use href="#G" transform="rotate(144)" /> </g> </svg>’) penrose(6) </syntaxhighlight> =={{header\|C++}}== Line 120 ⟶ 157: {{out}} [[Media:Penrose tiling cpp.svg]] ~~Writes a file in SVG format similar to that produced by the Perl solution.~~ =={{header\|EasyLang}}== [https://easylang.online/show/#cod=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 Run it] <syntaxhighlight> proc lsysexp level . axiom$ rules$[] . for l to level an$ = "" for c$ in strchars axiom$ for i = 1 step 2 to len rules$[] if rules$[i] = c$ c$ = rules$[i + 1] break 1 . . an$ &= c$ . swap axiom$ an$ . . stack[] = [ ] proc lsysdraw axiom$ x y ang lng . . linewidth 0.3 move x y for c$ in strchars axiom$ if c$ = "E" x += cos dir * lng y += sin dir * lng line x y elif c$ = "-" dir -= ang elif c$ = "+" dir += ang elif c$ = "[" stack[] &= x stack[] &= y stack[] &= dir elif c$ = "]" l = len stack[] x = stack[l - 2] y = stack[l - 1] dir = stack[l] len stack[] -3 move x y . . . axiom$ = "[b]++[b]++[b]++[b]++[b]" rules$[] = [ "a" "cE++dE----bE[-cE----aE]++" "b" "+cE--dE[---aE--bE]+" "c" "-aE++bE[+++cE++dE]-" "d" "--cE++++aE[+dE++++bE]--bE" "E" "" ] lsysexp 6 axiom$ rules$[] lsysdraw axiom$ 50 50 36 4 </syntaxhighlight> =={{header\|FreeBASIC}}== {{trans\|Phython}} Not much of a FreeBASIC program: majority of this code is string literals that dumps an SVG on output. <syntaxhighlight lang="vb">Sub penrose(depth As Integer) Dim As String svg svg = "<svg viewBox=""-100 -100 200 200"" xmlns=""http://www.w3.org/2000/svg"">" + !"\n" svg &= " <defs>" + !"\n" svg &= " <path id=""A0"" d=""M 80.90169943749474 58.778525229247315 L 0 0 100 0"" stroke=""black"" fill=""#8bc"" />" + !"\n" svg &= " <path id=""B0"" d=""M 0 0 80.90169943749474 58.778525229247315 161.80339887498948 0"" stroke=""black"" fill=""#97e"" />" + !"\n" For d As Integer = 0 To 5 svg &= " <g id=""A" : svg &= (d+1) : svg &= """ transform=""translate(100, 0) scale(0.6180339887498949)"">" + !"\n" svg += " <use href=" & """" & "#A" & d & """ transform=""rotate(108)"" />" + !"\n" svg &= " <use href=" & """" & "#B" & d & """ transform=""scale(-1, 1)"" />" + !"\n" svg &= " </g>" + !"\n" svg &= " <g id=""B" & d+1 & """>" + !"\n" svg &= " <use href=" & """" & "#A" & d+1 & """ />" + !"\n" svg &= " <use href=" & """" & "#B" & d & """ transform=""translate(100, 0) scale(0.6180339887498949) rotate(144) translate(-80.90169943749474,-58.778525229247315)""/>" + !"\n" svg &= " </g>" + !"\n" Next svg &= " <g id=""G"">" + !"\n" svg &= " <use href=""#A6""/>" + !"\n" svg &= " <use href=""#A6"" transform=""scale(1, -1)"" />" + !"\n" svg &= " </g>" + !"\n" svg &= " </defs>" + !"\n" svg &= " <g transform=""scale(2, 2)"">" + !"\n" svg &= " <use href=""#G"" transform=""rotate(-144)"" />" + !"\n" svg &= " <use href=""#G"" transform=""rotate(-72)"" />" + !"\n" svg &= " <use href=""#G"" transform=""rotate(0)"" />" + !"\n" svg &= " <use href=""#G"" transform=""rotate(72)"" />" + !"\n" svg &= " <use href=""#G"" transform=""rotate(144)"" />" + !"\n" svg &= " </g>" + !"\n" svg &= "</svg>" Print #1, svg End Sub Open "Penrose_tiling.svg" For Output As #1 penrose(6) Close #1</syntaxhighlight> =={{header\|Fōrmulæ}}== {{FormulaeEntry\|page=https://formulae.org/?script=examples/L-system}} '''Solution''' It can be done using an [[wp:L-system\|L-system]]. There are generic functions written in Fōrmulæ to compute an L-system in the page [[L-system#Fōrmulæ \| L-system]]. The program that creates a Penrose tiling is: [[File:Fōrmulæ - L-system - Penrose tiling 01.png]] [[File:Fōrmulæ - L-system - Penrose tiling 02.png]] =={{header\|Go}}== Line 1,446 ⟶ 1,591: {{libheader\|Wren-set}} {{libheader\|Wren-polygon}} <syntaxhighlight lang="~~ecmascript~~wren">import "graphics" for Canvas, Color import "dome" for Window import "math" for Math