Playing with scripting of the drawing app Intaglio, I made this nice picture: For the curious, here’s a script that will generate a similar tiling
property magicRatio : (1 + (5 ^ 0.5)) / 2
property invMagicRatio : 2 / (1 + (5 ^ 0.5))
property sinPiOverFive : 0.587785252
property sinTwoPiOverFive : 0.951056516
property cosTwoPiOverFive : 0.309016994
property cosPiOverFive : 0.809016994
to drawATriangle(pt1, pt2, pt3, width, fc)
tell application “Intaglio”
make new path with properties {segments:{move to, {x of pt1, y of pt1}, line to, {x of pt2, y of pt2}, line to, {x of pt3, y of pt3}, line to, {x of pt1, y of pt1}}, drawing mode:fill, stroke width:2, fill color:rgb & fc, stroke color:{rgb, 0.2, 0.2, 1, 0.4}}
end tell
end drawATriangle
to subdivideB(pt1, pt2, pt3, numSubdivisions)
set delX to (x of pt3) – (x of pt1)
set delY to (y of pt3) – (y of pt1)
set pt4 to {x:(x of pt3) – delX * invMagicRatio, y:(y of pt3) – delY * invMagicRatio}
if numSubdivisions is less than 5 then
set alpha to 0.9 – ((numSubdivisions) * 0.2)
drawATriangle(pt1, pt2, pt3, numSubdivisions, {0.3, 1, 0.4, alpha}) — change the colors here !!
end if
if (numSubdivisions > 1) then
subdivideA(pt2, pt3, pt4, numSubdivisions – 1)
end if
if (numSubdivisions > 2) then
subdivideB(pt2, pt4, pt1, numSubdivisions – 2)
end if
end subdivideB
to subdivideA(pt1, pt2, pt3, numSubdivisions)
set delX to (x of pt2) – (x of pt1)
set delY to (y of pt2) – (y of pt1)
set pt4 to {x:(x of pt2) – delX * invMagicRatio, y:(y of pt2) – delY * invMagicRatio}
if numSubdivisions is less than 5 then
set alpha to 0.9 – ((numSubdivisions) * 0.2)
drawATriangle(pt1, pt2, pt3, numSubdivisions, {0, 0.4, 1, alpha}) — change the colors here !!
end if
if (numSubdivisions > 2) then
subdivideA(pt4, pt3, pt1, numSubdivisions – 2)
end if
if (numSubdivisions > 1) then
subdivideB(pt2, pt4, pt3, numSubdivisions – 1)
end if
end subdivideA
set centerX to 280
set centerY to 350
set len to 280
— ptList is the ten outside points of the decagon, with the first one repeated at the end
set ptList to {{x:len, y:0}, {x:len * cosPiOverFive, y:len * sinPiOverFive}, {x:len * cosTwoPiOverFive, y:len * sinTwoPiOverFive}, {x:-len * cosTwoPiOverFive, y:len * sinTwoPiOverFive}, {x:-len * cosPiOverFive, y:len * sinPiOverFive}, {x:-len, y:0}, {x:-len * cosPiOverFive, y:-len * sinPiOverFive}, {x:-len * cosTwoPiOverFive, y:-len * sinTwoPiOverFive}, {x:len * cosTwoPiOverFive, y:-len * sinTwoPiOverFive}, {x:len * cosPiOverFive, y:-len * sinPiOverFive}, {x:len, y:0}}
set a to 1
repeat 5 times
set pt1 to {x:centerX, y:centerY}
set pt2 to {x:centerX + (x of item a of ptList), y:centerY + (y of item a of ptList)}
set a to a + 1
set pt3 to {x:centerX + (x of item a of ptList), y:centerY + (y of item a of ptList)}
subdivideA(pt3, pt1, pt2, 8 )
set a to a + 1
set pt2 to {x:centerX + (x of item a of ptList), y:centerY + (y of item a of ptList)}
subdivideA(pt3, pt1, pt2, 8 )
end repeat

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