The 2D-Harmonograph In Shiny

If you wish to make an apple pie from scratch, you must first invent the universe (Carl Sagan)

I like Shiny and I can’t stop converting into apps some of my previous experiments: today is the turn of the harmonograph. This is a simple application since you only can press a button to generate a random harmonograph-simulated curve. I love how easy is to create a nice interactive app to play with from an existing code. The only trick in this case in to add a rerun button in the UI side and transfer the interaction to the server side using a simple if. Very easy. This is a screenshot of the application:


Press the button and you will get a new drawing. Most of them are nice scrawls and from time to time you will obtain beautiful shapely curves.

And no more candy words: It is time to complain. I say to RStudio with all due respect, you are very cruel. You let me to deploy my previous app to your server but you suspended it almost immediately for fifteen days due to “exceeded usage hours”. My only option is paying at least $440 per year to upgrade my current plan. I tried the ambrosia for an extremely short time. RStudio: Why don’t you launch a cheaper account? Why don’t you launch a free account with just one perpetual alive app at a time? Why don’t you increase the usage hours threshold? I can help you to calculate the return on investment of these scenarios.

Or, Why don’t you make me a gift for my next birthday? I promise to upload a new app per month to promote your stunning tool. Think about it and please let me know your conclusions.

Meanwhile I will run the app privately. This is the code to do it:


# This is the user-interface definition of a Shiny web application.
# You can find out more about building applications with Shiny here:


  titlePanel("Mathematical Beauties: The Harmonograph"),

      # 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=\"\">here</a> to see an image of a real harmonograph</p>")
        actionButton('rerun','Launch the harmonograph!')


# This is the server logic for a Shiny web application.
# You can find out more about building applications with Shiny here:


CreateDS = function () 
  f=jitter(sample(c(2,3),4, replace = TRUE))
  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))}

shinyServer(function(input, output) {
    dat<-reactive({if (input$rerun) dat=CreateDS() else dat=CreateDS()})
   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)

9 thoughts on “The 2D-Harmonograph In Shiny

  1. You do so many cool things on this blog, super impressive! I’ve also had problems with that my shiny app goes down after a few days, but I guess they have to pay for servers somehow… One way of making shiny app easier to run is to put both the UI and the server into the same script. Here is a rearranged version of you harmonograph that you can directly copy-n-paste into an R console:


      1. The awkward `if (input$rerun)` code can be improved using `eventReactive`:
        dat<-eventReactive(input$rerun, { CreateDS() })

  2. This is very cool work. I work at RStudio and thought I would reach out since it is definitely not our intention to be cruel. 🙂 We have been toying with an additional option for pricing that I would love to chat with you about and get your take on. Will try to reach you directly on Twitter.

Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s