An example of doing prolonged, iterative computation in Shiny. Adapted from: https://gist.github.com/trestletech/8608815

iterative-comp-shiny.R

library(shiny)

ui <- fluidPage(
  sidebarLayout(
    sidebarPanel(
      numericInput("steps", "Time steps:", 10, min=1),
      actionButton("run", label="Start")
    ),
    mainPanel(
      textOutput("status")
    )
  )
)


server <- function(input, output, session) {
  
  vals <- reactiveValues(running = FALSE, step = 0, run = 1, label = "Start")
  
  # helper functions
  toggleLabel <- function() {
    if (vals$label %in% c("Start", "Resume")) vals$label <- "Stop"
    else vals$label <- "Resume"
    vals$label
  }
  
  observe({
    req(input$run)
    
    isolate({
      # update label when the button is clicked and stop/resume computation
      if (input$run != vals$run) {
        updateActionButton(session, "run", label = toggleLabel())
        vals$run <- input$run
        vals$running <- !vals$running
      }
      
      # update label and vals$running the first time around only
      if (vals$label == "Start") {
        updateActionButton(session, "run", label = toggleLabel())
        vals$running <- TRUE
      }
    })
    
    # If we're not done yet, then schedule this block to execute again ASAP.
    # Note that we can be interrupted by other reactive updates to, for
    # instance, update a text output.
    if (isolate({ (vals$step < input$steps) && vals$running })) {
      Sys.sleep(1) # placeholder for computation
      vals$step <- isolate(vals$step) + 1
      invalidateLater(0, session)
    }
  })
  
  output$status <- renderText({
    paste("You're on iteration number:", vals$step)
  })
}

shinyApp(ui, server)