# 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 $440 per year to upgrade my current plan. I tried the ambrosia for an extremely short time. RStudio: Why don’t you launch a cheaper account? Why don’t you launch a free account with just one perpetual alive app at a time? Why don’t you increase the usage hours threshold? I can help you to calculate the return on investment of these scenarios. Or, Why don’t you make me a gift for my next birthday? I promise to upload a new app per month to promote your stunning tool. Think about it and please let me know your conclusions. Meanwhile I will run the app privately. This is the code to do it: UI.R # This is the user-interface definition of a Shiny web application. # You can find out more about building applications with Shiny here: # # http://www.rstudio.com/shiny/ library(shiny) shinyUI(fluidPage( titlePanel("Mathematical Beauties: The Harmonograph"), sidebarLayout( sidebarPanel( #helpText(), # adding the new div tag to the sidebar tags$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.R

# This is the server logic for a Shiny web application.
# You can find out more about building applications with Shiny here:
#
# http://www.rstudio.com/shiny/
#

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))}

shinyServer(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)
})

# Shiny Wool Skeins

Chaos is not a pit: chaos is a ladder (Littlefinger in Game of Thrones)

Some time ago I wrote this post to show how my colleague Vu Anh translated into Shiny one of my experiments, opening my eyes to an amazing new world. I am very proud to present you the first Shiny experiment entirely written by me.

In this case I took inspiration from another previous experiment to draw some kind of wool skeins. The shiny app creates a plot consisting of chords inside a circle. There are to kind of chords:

• Those which form a track because they are a set of glued chords; number of tracks and number of chords per track can be selected using Number of track chords and Number of scrawls per track sliders of the app respectively.
• Those forming the background, randomly allocated inside the circle. Number of background chords can be chosen as well in the app

There is also the possibility to change colors of chords. This are the main steps I followed to build this Shiny app:

1. Write a simple R program
2. Decide which variables to parametrize
3. Open a new Shiny project in RStudio
4. Analize the sample UI.R and server.R files generated by default
5. Adapt sample code to my particular code (some iterations are needed here)
6. Deploy my app in the Shiny Apps free server

Number 1 is the most difficult step, but it does not depends on Shiny: rest of them are easier, specially if you have help as I had from my colleague Jorge. I encourage you to try. This is an snapshot of the app:

You can play with the app here.

Some things I thought while developing this experiment:

• Shiny gives you a lot with a minimal effort
• Shiny can be a very interesting tool to teach maths and programming to kids
• I have to translate to Shiny some other experiment
• I will try to use it for my job

Try Shiny: is very entertaining. A typical Shiny project consists on two files, one to define the user interface (UI.R) and the other to define the back end side (server.R).

This is the code of UI.R:

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

library(shiny)

shinyUI(fluidPage(

# Application title
titlePanel("Shiny Wool Skeins"),
HTML("<p>This experiment is based on <a href=\"https://aschinchon.wordpress.com/2015/05/13/bertrand-or-the-importance-of-defining-problems-properly/\">this previous one</a> I did some time ago. It is my second approach to the wonderful world of Shiny.</p>"),
# Sidebar with a slider input for number of bins
sidebarLayout(
sidebarPanel(
inputPanel(
sliderInput("lin", label = "Number of track chords:",
min = 1, max = 20, value = 5, step = 1),
sliderInput("rep", label = "Number of scrawls per track:",
min = 1, max = 50, value = 10, step = 1),
sliderInput("nbc", label = "Number of background chords:",
min = 0, max = 2000, value = 500, step = 2),
selectInput("col1", label = "Track colour:",
choices = colors(), selected = "darkmagenta"),
selectInput("col2", label = "Background chords colour:",
choices = colors(), selected = "gold")
)

),

# Show a plot of the generated distribution
mainPanel(
plotOutput("chordplot")
)
)
))

And this is the code of server.R:

# This is the server logic for a Shiny web application.
# You can find out more about building applications with Shiny here:
#
# http://shiny.rstudio.com
#
library(ggplot2)
library(magrittr)
library(grDevices)
library(shiny)

shinyServer(function(input, output) {

df<-reactive({
ini=runif(n=input$lin, min=0,max=2*pi) ini %>% +runif(n=input$lin, min=pi/2,max=3*pi/2) %>%
cbind(ini, end=.) %>%
as.data.frame() -> Sub1
Sub1=Sub1[rep(seq_len(nrow(Sub1)), input$rep),] Sub1 %>% apply(c(1, 2), jitter) %>% as.data.frame() -> Sub1 Sub1=with(Sub1, data.frame(col=input$col1, x1=cos(ini), y1=sin(ini), x2=cos(end), y2=sin(end)))
Sub2=runif(input$nbc, min = 0, max = 2*pi) Sub2=data.frame(x=cos(Sub2), y=sin(Sub2)) Sub2=cbind(input$col2, Sub2[(1:(input$nbc/2)),], Sub2[(((input$nbc/2)+1):input$nbc),]) colnames(Sub2)=c("col", "x1", "y1", "x2", "y2") rbind(Sub1, Sub2) }) opts=theme(legend.position="none", panel.background = element_rect(fill="white"), panel.grid = element_blank(), axis.ticks=element_blank(), axis.title=element_blank(), axis.text =element_blank()) output$chordplot<-renderPlot({
p=ggplot(df())+geom_segment(aes(x=x1, y=y1, xend=x2, yend=y2), colour=df()$col, alpha=runif(nrow(df()), min=.1, max=.3), lwd=1)+opts;print(p) }, height = 600, width = 600 ) }) # Simple Data Science To Maximize Return On Lottery Investment Every finite game has an equilibrium point (John Nash, Non-Cooperative Games, 1950) I read recently this amazing book, where I discovered that we (humans) are not capable of generating random sequences of numbers by ourselves when we play lottery. John Haigh demonstrates this fact analyzing a sample of 282 raffles of 6/49 UK Lotto. Once I read this, I decided to prove if this disability is property only of British population or if it is shared with Spanish people as well. I am Spanish, so this experiment can bring painful results to myself, but here I come. The Spanish equivalent of 6/40 UK Lotto is called “Lotería Primitiva” (or “Primitiva”, to abbreviate). This is a ticket of Primitiva lotto: As you can see, one ticket gives the chance to do 8 bets. Each bet consists on 6 numbers between 1 and 49 to be chosen in a grid of 10 rows by 5 columns. People tend to choose separate numbers because we think that they are more likely to come up than combinations with some consecutive numbers. We think we have more chances to get rich choosing 4-12-23-25-31-43 rather than 3-17-18-19-32-33, for instance. To be honest, I should recognize I am one of these persons. Primitiva lotto is managed by Sociedad Estatal Loterías y Apuestas del Estado, a public business entity belonging to the Spanish Ministry of Finance and Public Administrations. They know what people choose and they could do this experiment more exactly than me. They could analyze just human bets (those made by players by themselves) and discard machine ones (those made automatically by vending machines) but anyway it is possible to confirm the previous thesis with some public data. I analysed 432 raffles of Primitiva carried out between 2011 and 2015; for each raffle I have this information: • The six numbers that form the winning combination • Total number of bets • Number of bets which hit the six numbers (Observed Winners) The idea is to compare observed winners of raffles with the expected number of them, estimated as follows: $Expected\, Winners=\frac{Total\, Bets}{C_{6}^{49}},\: where\: C_{6}^{49}=\binom{49}{6}=\frac{49!}{43!6!}$ This table compare the number of expected and observed winners between raffles which contain consecutive and raffles which not: There are 214 raffles without consecutive with 294 winners while the expected number of them was 219. In other words, a winner of a non-consecutive-raffle must share the prize with a 33% of some other person. On the other hand, the number of observed winners of a raffle with consecutive numbers 17% lower than the expected one. Simple and conclusive. Spanish are like British, at least in what concerns to this particular issue. Let’s go further. I can do the same for any particular number. For example, there were 63 raffles containing number 45 in the winning combination and 57 (observed) winners, although 66 were expected. After doing this for every number, I can draw this plot, where I paint in blue those which ratio of observed winners between expected is lower than 0.9: It seems that blue numbers are concentrated on the right side of the grid. Do we prefer small numbers rather than big ones? There are 15 primes between 1 and 49 (rate: 30%) but only 3 primes between blue numbers (rate: 23%). Are we attracted by primes? Let’s combine both previous results. This table compares the number of expected and observed winners between raffles which contain consecutive and blues (at least one) and raffles which not: Now, winning combinations with some consecutive and some blue numbers present 20% less of observed winners than expected. After this, which combination would you choose for your next bet? 27-35-36-41-44-45 or 2-6-13-15-26-28? I would choose the first one. Both of them have the same probability to come up, but probably you will become richer with the first one if it happens. This is the code of this experiment. If someone need the dataset set to do their own experiments, feel free to ask me (you can find my email here): library("xlsx") library("sqldf") library("Hmisc") library("lubridate") library("ggplot2") library("extrafont") library("googleVis") windowsFonts(Garamond=windowsFont("Garamond")) setwd("YOUR WORKING DIRECTORY HERE") file = "SORTEOS_PRIMITIVA_2011_2015.xls" data=read.xlsx(file, sheetName="ALL", colClasses=c("numeric", "Date", rep("numeric", 21))) #Impute null values to zero data$C1_EUROS=with(data, impute(C1_EUROS, 0))
data$CE_WINNERS=with(data, impute(CE_WINNERS, 0)) #Expected winners for each raffle data$EXPECTED=data$BETS/(factorial(49)/(factorial(49-6)*factorial(6))) #Consecutives indicator data$DIFFMIN=apply(data[,3:8], 1, function (x) min(diff(sort(x))))
#Consecutives vs non-consecutives comparison
df1=sqldf("SELECT CASE WHEN DIFFMIN=1 THEN 'Yes' ELSE 'No' END AS CONS,
COUNT(*) AS RAFFLES,
SUM(EXPECTED) AS EXP_WINNERS,
SUM(CE_WINNERS+C1_WINNERS) AS OBS_WINNERS
FROM data GROUP BY CONS")
colnames(df1)=c("Contains consecutives?", "Number of  raffles", "Expected Winners", "Observed Winners")
Table1=gvisTable(df1, formats=list('Expected Winners'='#,###'))
plot(Table1)
#Heat map of each number
results=data.frame(BALL=numeric(0), EXP_WINNER=numeric(0), OBS_WINNERS=numeric(0))
for (i in 1:49)
{
data$TF=apply(data[,3:8], 1, function (x) i %in% x + 0) v=data.frame(BALL=i, sqldf("SELECT SUM(EXPECTED) AS EXP_WINNERS, SUM(CE_WINNERS+C1_WINNERS) AS OBS_WINNERS FROM data WHERE TF = 1")) results=rbind(results, v) } results$ObsByExp=results$OBS_WINNERS/results$EXP_WINNERS
results$ROW=results$BALL%%10+1
results$COL=floor(results$BALL/10)+1
results$ObsByExp2=with(results, cut(ObsByExp, breaks=c(-Inf,.9,Inf), right = FALSE)) opt=theme(legend.position="none", panel.background = element_blank(), panel.grid = element_blank(), axis.ticks=element_blank(), axis.title=element_blank(), axis.text =element_blank()) ggplot(results, aes(y=ROW, x=COL)) + geom_tile(aes(fill = ObsByExp2), colour="gray85", lwd=2) + geom_text(aes(family="Garamond"), label=results$BALL, color="gray10", size=12)+
scale_fill_manual(values = c("dodgerblue", "gray98"))+
scale_y_reverse()+opt
#Blue numbers
Bl=subset(results, ObsByExp2=="[-Inf,0.9)")[,1]
data\$BLUES=apply(data[,3:8], 1, function (x) length(intersect(x,Bl)))
#Combination of consecutives and blues
df2=sqldf("SELECT CASE WHEN DIFFMIN=1 AND BLUES>0 THEN 'Yes' ELSE 'No' END AS IND,
COUNT(*) AS RAFFLES,
SUM(EXPECTED) AS EXP_WINNERS,
SUM(CE_WINNERS+C1_WINNERS) AS OBS_WINNERS
FROM data GROUP BY IND")
colnames(df2)=c("Contains consecutives and blues?", "Number of  raffles", "Expected Winners", "Observed Winners")
Table2=gvisTable(df2, formats=list('Expected Winners'='#,###'))
plot(Table2)