148 lines
3.8 KiB
AppleScript
148 lines
3.8 KiB
AppleScript
-- SIERPINSKI TRIANGLE BY XOR / RULE 90 --------------------------------------
|
|
|
|
-- sierpinskiTriangle :: Int -> String
|
|
on sierpinskiTriangle(intOrder)
|
|
|
|
-- A Sierpinski triangle of order N
|
|
-- is a Pascal triangle (of N^2 rows)
|
|
-- mod 2
|
|
|
|
-- pascalModTwo :: Int -> [[String]]
|
|
script pascalModTwo
|
|
on |λ|(intRows)
|
|
|
|
-- addRow [[Int]] -> [[Int]]
|
|
script addRow
|
|
|
|
-- nextRow :: [Int] -> [Int]
|
|
on nextRow(row)
|
|
-- The composition of AsciiBinary . mod two . add
|
|
-- is reduced here to a rule from
|
|
-- two parent characters above,
|
|
-- to the child character below.
|
|
|
|
-- Rule 90 also reduces to this XOR relationship
|
|
-- between left and right neighbours.
|
|
|
|
-- rule :: Character -> Character -> Character
|
|
script rule
|
|
on |λ|(a, b)
|
|
if a = b then
|
|
space
|
|
else
|
|
"*"
|
|
end if
|
|
end |λ|
|
|
end script
|
|
|
|
zipWith(rule, {" "} & row, row & {" "})
|
|
end nextRow
|
|
|
|
on |λ|(xs)
|
|
xs & {nextRow(item -1 of xs)}
|
|
end |λ|
|
|
end script
|
|
|
|
foldr(addRow, {{"*"}}, enumFromTo(1, intRows - 1))
|
|
end |λ|
|
|
end script
|
|
|
|
-- The centring foldr (fold right) below starts from the end of the list,
|
|
-- (the base of the triangle) which has zero indent.
|
|
|
|
-- Each preceding row has one more indent space than the row below it.
|
|
|
|
script centred
|
|
on |λ|(sofar, row)
|
|
set strIndent to indent of sofar
|
|
|
|
{triangle:strIndent & intercalate(space, row) & linefeed & ¬
|
|
triangle of sofar, indent:strIndent & space}
|
|
end |λ|
|
|
end script
|
|
|
|
triangle of foldr(centred, {triangle:"", indent:""}, ¬
|
|
pascalModTwo's |λ|(intOrder ^ 2))
|
|
|
|
end sierpinskiTriangle
|
|
|
|
|
|
-- TEST ----------------------------------------------------------------------
|
|
on run
|
|
|
|
set strTriangle to sierpinskiTriangle(4)
|
|
|
|
set the clipboard to strTriangle
|
|
strTriangle
|
|
end run
|
|
|
|
|
|
-- GENERIC FUNCTIONS ---------------------------------------------------------
|
|
|
|
-- enumFromTo :: Int -> Int -> [Int]
|
|
on enumFromTo(m, n)
|
|
if m > n then
|
|
set d to -1
|
|
else
|
|
set d to 1
|
|
end if
|
|
set lst to {}
|
|
repeat with i from m to n by d
|
|
set end of lst to i
|
|
end repeat
|
|
return lst
|
|
end enumFromTo
|
|
|
|
-- foldr :: (a -> b -> a) -> a -> [b] -> a
|
|
on foldr(f, startValue, xs)
|
|
tell mReturn(f)
|
|
set v to startValue
|
|
set lng to length of xs
|
|
repeat with i from lng to 1 by -1
|
|
set v to |λ|(v, item i of xs, i, xs)
|
|
end repeat
|
|
return v
|
|
end tell
|
|
end foldr
|
|
|
|
-- intercalate :: Text -> [Text] -> Text
|
|
on intercalate(strText, lstText)
|
|
set {dlm, my text item delimiters} to {my text item delimiters, strText}
|
|
set strJoined to lstText as text
|
|
set my text item delimiters to dlm
|
|
return strJoined
|
|
end intercalate
|
|
|
|
-- min :: Ord a => a -> a -> a
|
|
on min(x, y)
|
|
if y < x then
|
|
y
|
|
else
|
|
x
|
|
end if
|
|
end min
|
|
|
|
-- Lift 2nd class handler function into 1st class script wrapper
|
|
-- mReturn :: Handler -> Script
|
|
on mReturn(f)
|
|
if class of f is script then
|
|
f
|
|
else
|
|
script
|
|
property |λ| : f
|
|
end script
|
|
end if
|
|
end mReturn
|
|
|
|
-- zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
|
|
on zipWith(f, xs, ys)
|
|
set lng to min(length of xs, length of ys)
|
|
set lst to {}
|
|
tell mReturn(f)
|
|
repeat with i from 1 to lng
|
|
set end of lst to |λ|(item i of xs, item i of ys)
|
|
end repeat
|
|
return lst
|
|
end tell
|
|
end zipWith
|