Using Elm architecture and setting random seed.

Random.elm

import Time
import Random

import Html exposing (..)
import Html.Attributes exposing (..)
import Html.Events exposing (..)


-- MODEL

type alias Model = 
  { random : Int
  , seed : Random.Seed
  }
  
init = { random = 0, seed = Random.initialSeed 0 }


-- UPDATE

type Action = GenRandom

update : Action -> Model -> Model
update action model = 
  case action of 
    GenRandom -> 
      let
        (random, seed') = Random.generate (Random.int 0 100) model.seed
      in
        { model | random <- random, seed <- seed' }


-- VIEW

view : Signal.Address Action -> Model -> Html
view address model = 
  div [] 
    [ text (toString model.random) 
    , text (toString model.seed)
    , hr [] []
    , button [ onClick address GenRandom ] [ text "Generate random" ]
    ]


-- WIRING

main = 
  let
    action = Signal.mailbox Nothing
    
    address = Signal.forwardTo action.address Just
    
    currentTime = Time.every Time.second
    
    model = Signal.foldp 
      (\(Just action) model -> update action model)
      init
      action.signal
      
    model' = Signal.map2 
      (\model time -> { model | seed <- Random.initialSeed (round time) })
      model
      currentTime
  in
    Signal.map (view address) model'