Sierpinski pentagon: Difference between revisions

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pentaflake order = iterate transformation pentagon !! order

where

transformation = Scale s s . foldMap copy [0..4]

transformation = Scale s s . foldMap copy [0,72..288]

copy i = Rotate ~~(72*i)~~ . Translate 0 x

copy a = Rotate a . Translate 0 x

pentagon = Polygon [ (sin a, cos a) | a <- [0,2*pi/5..2*pi] ]

x = 2*cos(pi/5)

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where dc = InWindow "Pentaflake" (400, 400) (0, 0)</lang>

'''Explanation''': Since <tt>Picture</tt> forms a monoid with image overlaying as multiplication, so do functions having type <tt>Picture -> Picture</tt>:

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See also implementation using [http://projects.haskell.org/diagrams/gallery/Pentaflake.html Diagrams]

f,g :: Picture -> Picture

f <> g = \p -> f p <> g p

Function <code>copy</code> for an angle returns transformation, which shifts and rotates given picture, therefore <code>foldMap copy</code> for a list of angles returns a transformation, which shifts and rotates initial image five times. After that the resulting image is scaled to fit the inital size, so that it is ready for next iteration.

If one wants to get all intermediate pentaflakes <code>transformation</code> shoud be changed as follows:

<lang haskell>transformation = Scale s s . (Rotate 36 <> foldMap copy [0,72..288])</lang>

⚫

See also the implementation using [http://projects.haskell.org/diagrams/gallery/Pentaflake.html Diagrams]

=={{header|Java}}==