Fractal construction with pentagons.

Author: Brent Yorgey

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> {-# LANGUAGE NoMonomorphismRestriction #-}
> import Diagrams.Prelude

A \(0\)-pentaflake is just a regular pentagon:

> grad = defaultRG & _RG . rGradStops .~ mkStops [(blue,0,1), (crimson,1,1)]
>                  & _RG . rGradRadius1 .~ 50
> pentaflake' 0 = regPoly 5 1 # lw none

An \(n\)-pentaflake is an \((n-1)\)-pentaflake surrounded by five more. The appends function is useful here for positioning the five pentaflakes around the central one.

> pentaflake' n = appends
>                   pCenter
>                   (zip vs (repeat (rotateBy (1/2) pOutside)))
>   where vs = iterateN 5 (rotateBy (1/5))
>            . (if odd n then negateV else id)
>            $ unitY
>         pCenter  = pentaflake' (n-1)
>         pOutside = pCenter # opacity (1.7 / fromIntegral n)
> 
> pentaflake n = pentaflake' n # fillTexture grad # bg silver

A \(4\)-pentaflake looks nice. Of course there’s an exponential blowup in the number of primitives, so generating higher-order pentaflakes can take a long time!

> example = pentaflake 4