ParticleRainbow.hs

import Diagrams.Prelude

import Diagrams.Backend.Cairo

import Data.Colour.RGBSpace.HSV
import Data.Colour.SRGB.Linear

import Data.Numbers.Primes

import Control.Monad

import Text.Printf

trajectory :: Int -> Double -> P2 Double
trajectory i t = cos (t*k*pi) ^& sin (t*k'*pi)
 where (k:k':_) = fromIntegral<$>(drop i primes :: [Int])

droplet :: Double -> P2 Double -> Diagram B
droplet r p@(P (V2 _ y))
   = circle r
       & moveTo p
       & fc ptcColour
       & lc ptcColour
 where ptcColour = rgb r g b
        where RGB r g b = hsv ((y+1)*160) 1 1

srate :: Num n => n
srate = 200

rainbowsnap :: Double -> Diagram B
rainbowsnap t
    = mconcat [ droplet 0.05 (trajectory (round $ 12 - 0.3*j) $ tanh (t'*(4+j*3)))
              | j <- [0 .. 30]
              , t' <- let oversampling = 40
                      in [t + j/(oversampling*srate) | j<-[1..oversampling]] ]
          <> (rect 5 3 & fc black)

main :: IO ()
main = do
   forM_ [0 .. 2*srate] $ \i -> do
    let t = fromIntegral (i :: Int) / srate - 1
    renderCairo
     (printf "rainbow_%03i.png" i)
     (dims $ 300 ^& 180)
     (rainbowsnap t)

https://physics.stackexchange.com/a/638745/3540