Harmonograf in Shiny by Antonio S. Chinchón from https://aschinchon.wordpress.com/2015/06/23/the-2d-harmonograph-in-shiny/

shiny_harmonograph.R

# From https://aschinchon.wordpress.com/2015/06/23/the-2d-harmonograph-in-shiny/
# All code by Antonio S. Chinchón (@aschinchon), just rearranged so that you can directly
# run it by copy and pasting it into an R console.

library(shiny)
CreateDS = function () {
  f=jitter(sample(c(2,3),4, replace = TRUE))
  d=runif(4,0,1e-02)
  p=runif(4,0,pi)
  xt = function(t) exp(-d[1]*t)*sin(t*f[1]+p[1])+exp(-d[2]*t)*sin(t*f[2]+p[2])
  yt = function(t) exp(-d[3]*t)*sin(t*f[3]+p[3])+exp(-d[4]*t)*sin(t*f[4]+p[4])
  t=seq(1, 200, by=.0005)
  data.frame(t=t, x=xt(t), y=yt(t))
}

  shinyApp(
    ui = fluidPage(
  titlePanel("Mathematical Beauties: The Harmonograph"),
  sidebarLayout(
    sidebarPanel(
      #helpText(),
 
      # adding the new div tag to the sidebar            
      tags$div(class="header", checked=NA,
               tags$p("A harmonograph is a mechanical apparatus that employs pendulums to create a 
                       geometric image. The drawings created typically are Lissajous curves, or 
                       related drawings of greater complexity. The devices, which began to appear 
                       in the mid-19th century and peaked in popularity in the 1890s, cannot be 
                       conclusively attributed to a single person, although Hugh Blackburn, a professor 
                       of mathematics at the University of Glasgow, is commonly believed to be the official 
                       inventor. A simple, so-called \"lateral\" harmonograph uses two pendulums to control the movement 
                       of a pen relative to a drawing surface. One pendulum moves the pen back and forth along 
                       one axis and the other pendulum moves the drawing surface back and forth along a 
                       perpendicular axis. By varying the frequency and phase of the pendulums relative to 
                       one another, different patterns are created. Even a simple harmonograph as described 
                       can create ellipses, spirals, figure eights and other Lissajous figures (Source: Wikipedia)")),
               tags$div(class="header", checked=NA,
                       HTML("<p>Click <a href=\"http://paulbourke.net/geometry/harmonograph/harmonograph3.html\">here</a> to see an image of a real harmonograph</p>")
               ),
        actionButton('rerun','Launch the harmonograph!')
    ),
    mainPanel(
      plotOutput("HarmPlot")
    )
  )
),
    server = function(input, output) {
    dat<-reactive({if (input$rerun) dat=CreateDS() else dat=CreateDS()})
 output$HarmPlot<-renderPlot({
   plot(rnorm(1000),xlim =c(-2,2), ylim =c(-2,2), type="n")
   with(dat(), plot(x,y, type="l", xlim =c(-2,2), ylim =c(-2,2), xlab = "", ylab = "", xaxt='n', yaxt='n', col="gray10", bty="n"))
  }, height = 650, width = 650)
}
  )