(This article was first published on

**Ripples**, and kindly contributed to R-bloggers)Antonio, you don’t know what empathy is! (Cecilia, my beautiful wife)

Spirals are nice. In the wake of my previous post I have done a Shiny app to explore patterns generated by changing angle, shape and number of points of Fermat’s spiral equation. You can obtain an *almost infinite* number of images. This is just an example:

I like thinking in imaginary flowers. This is why I called this experiment *Phyllotaxis*.

More examples:

Just one comment about code: I did the Shiny in just one R file as this guy suggested me some time ago because of this post.

This is the code. Do your own imaginary flowers:

library(shiny) library(ggplot2) CreatePlot = function (ang=pi*(3-sqrt(5)), nob=150, siz=15, alp=0.8, sha=16, col="black", bac="white") { ggplot(data.frame(r=sqrt(1:nob), t=(1:nob)*ang*pi/180), aes(x=r*cos(t), y=r*sin(t)))+ geom_point(colour=col, alpha=alp, size=siz, shape=sha)+ scale_x_continuous(expand=c(0,0), limits=c(-sqrt(nob)*1.4, sqrt(nob)*1.4))+ scale_y_continuous(expand=c(0,0), limits=c(-sqrt(nob)*1.4, sqrt(nob)*1.4))+ theme(legend.position="none", panel.background = element_rect(fill=bac), panel.grid=element_blank(), axis.ticks=element_blank(), axis.title=element_blank(), axis.text=element_blank())} shinyApp( ui = fluidPage( titlePanel("Phyllotaxis by Shiny"), fluidRow( column(3, wellPanel( selectInput("col", label = "Colour of points:", choices = colors(), selected = "black"), selectInput("bac", label = "Background colour:", choices = colors(), selected = "white"), selectInput("sha", label = "Shape of points:", choices = list("Empty squares" = 0, "Empty circles" = 1, "Empty triangles"=2, "Crosses" = 3, "Blades"=4, "Empty diamonds"=5, "Inverted empty triangles"=6, "Bladed squares"=7, "Asterisks"=8, "Crosed diamonds"=9, "Crossed circles"=10, "Stars"=11, "Cubes"=12, "Bladed circles"=13, "Filled squares" = 15, "Filled circles" = 16, "Filled triangles"=17, "Filled diamonds"=18), selected = 16), sliderInput("ang", label = "Angle (degrees):", min = 0, max = 360, value = 180*(3-sqrt(5)), step = .05), sliderInput("nob", label = "Number of points:", min = 1, max = 1500, value = 60, step = 1), sliderInput("siz", label = "Size of points:", min = 1, max = 60, value = 10, step = 1), sliderInput("alp", label = "Transparency:", min = 0, max = 1, value = .5, step = .01) ) ), mainPanel( plotOutput("Phyllotaxis") ) ) ), server = function(input, output) { output$Phyllotaxis=renderPlot({ CreatePlot(ang=input$ang, nob=input$nob, siz=input$siz, alp=input$alp, sha=as.numeric(input$sha), col=input$col, bac=input$bac) }, height = 650, width = 650 )} )

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