# Chaotic Galaxies

Tell me, which side of the earth does this nose come from? Ha! (ALF)

Reading about strange attractors I came across with this book, where I discovered a way to generate two dimensional chaotic maps. The generic equation is pretty simple:

$x_{n+1}= a_{1}+a_{2}x_{n}+a_{3}x_{n}^{2}+a_{4}x_{n}y_{n}+a_{5}y_{n}+a_{6}y_{n}^{2}$
$y_{n+1}= a_{7}+a_{8}x_{n}+a_{9}x_{n}^{2}+a_{10}x_{n}y_{n}+a_{11}y_{n}+a_{12}y_{n}^{2}$

I used it to generate these chaotic galaxies:

Changing the vector of parameters you can obtain other galaxies. Do you want to try?

library(ggplot2)
library(dplyr)
#Generic function
attractor = function(x, y, z)
{
c(z[1]+z[2]*x+z[3]*x^2+ z[4]*x*y+ z[5]*y+ z[6]*y^2,
z[7]+z[8]*x+z[9]*x^2+z[10]*x*y+z[11]*y+z[12]*y^2)
}
#Function to iterate the generic function over the initial point c(0,0)
galaxy= function(iter, z)
{
df=data.frame(x=0,y=0)
for (i in 2:iter) df[i,]=attractor(df[i-1, 1], df[i-1, 2], z)
df %>% rbind(data.frame(x=runif(iter/10, min(df$x), max(df$x)),
y=runif(iter/10, min(df$y), max(df$y))))-> df
return(df)
}
opt=theme(legend.position="none",
panel.background = element_rect(fill="#00000c"),
plot.background = element_rect(fill="#00000c"),
panel.grid=element_blank(),
axis.ticks=element_blank(),
axis.title=element_blank(),
axis.text=element_blank(),
plot.margin=unit(c(-0.1,-0.1,-0.1,-0.1), "cm"))
#First galaxy
z1=c(1.0, -0.1, -0.2,  1.0,  0.3,  0.6,  0.0,  0.2, -0.6, -0.4, -0.6,  0.6)
galaxy1=galaxy(iter=2400, z=z1) %>% ggplot(aes(x,y))+
geom_point(shape= 8, size=jitter(12, factor=4), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=16, size= jitter(4, factor=2), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=46, size= 0, color="#ffff00")+opt
#Second galaxy
z2=c(-1.1, -1.0,  0.4, -1.2, -0.7,  0.0, -0.7,  0.9,  0.3,  1.1, -0.2,  0.4)
galaxy2=galaxy(iter=2400, z=z2) %>% ggplot(aes(x,y))+
geom_point(shape= 8, size=jitter(12, factor=4), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=16, size= jitter(4, factor=2), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=46, size= 0, color="#ffff00")+opt
#Third galaxy
z3=c(-0.3,  0.7,  0.7,  0.6,  0.0, -1.1,  0.2, -0.6, -0.1, -0.1,  0.4, -0.7)
galaxy3=galaxy(iter=2400, z=z3) %>% ggplot(aes(x,y))+
geom_point(shape= 8, size=jitter(12, factor=4), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=16, size= jitter(4, factor=2), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=46, size= 0, color="#ffff00")+opt
#Fourth galaxy
z4=c(-1.2, -0.6, -0.5,  0.1, -0.7,  0.2, -0.9,  0.9,  0.1, -0.3, -0.9,  0.3)
galaxy4=galaxy(iter=2400, z=z4) %>% ggplot(aes(x,y))+
geom_point(shape= 8, size=jitter(12, factor=4), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=16, size= jitter(4, factor=2), color="#ffff99", alpha=jitter(.05, factor=2))+
geom_point(shape=46, size= 0, color="#ffff00")+opt



# The Breathtaking 1-Matrix

La luna sale a caminar siguiendo tus pupilas (Ojos color sol, Calle 13)

This is a 5×5 1-matrix:

$\begin{bmatrix} 1 &1 &1 &1 &1 \\ 1 &1 &1 &1 &1 \\ 1 &1 &1 &1 &1 \\ 1 &1 &1 &1 &1 \\ 1 &1 &1 &1 &1 \end{bmatrix}$

And this is a 20×20 1-matrix visualized:

Maybe in some other galaxy, aliens represent matrix in this way.

par(mar = c(1, 1, 1, 1), bg="violetred4")
circlize::chordDiagram(matrix(1, 20, 20),
col="white",
symmetric = TRUE,
transparency = 0.85,
annotationTrack = NULL)


# Gummy Worms

Just keep swimming (Dory in Finding Nemo)

Inspired by this post, I decided to create gummy worms like this:

Or these:

When I was young I used to eat them.

Do you want to try? This is the code:

library(rgl)
library(RColorBrewer)
t=seq(1, 6, by=.04)
f = function(a, b, c, d, e, f, t) exp(-a*t)*sin(t*b+c)+exp(-d*t)*sin(t*e+f)
v1=runif(6,0,1e-02)
v2=runif(6, 2, 3)
v3=runif(6,-pi/2,pi/2)
open3d()
spheres3d(x=f(v1[1], v2[1], v3[1], v1[4], v2[4], v3[4], t),
y=f(v1[2], v2[2], v3[2], v1[5], v2[5], v3[5], t),
z=f(v1[3], v2[3], v3[3], v1[6], v2[6], v3[6], t),


# Playing With Julia (Set)

Viento, me pongo en movimiento y hago crecer las olas del mar que tienes dentro (Tercer Movimiento: Lo de Dentro, Extremoduro)

I really enjoy drawing complex numbers: it is a huge source of entertainment for me. In this experiment I play with the Julia Set, another beautiful fractal like this one. This is what I have done:

• Choosing the function f(z)=exp(z3)-0.621
• Generating a grid of complex numbers with both real and imaginary parts in [-2, 2]
• Iterating f(z) over the grid a number of times so zn+1 = f(zn)
• Drawing the resulting grid as I did here
• Gathering all plots into a GIF with ImageMagick as I did in my previous post: each frame corresponds to a different number of iterations

This is the result:

I love how easy is doing difficult things in R. You can play with the code changing f(z) as well as color palettes. Be ready to get surprised:

library(ggplot2)
library(dplyr)
library(RColorBrewer)
dir.create("output")
setwd("output")
f = function(z,c) exp(z^3)+c
# Grid of complex
z0 <- outer(seq(-2, 2, length.out = 1200),1i*seq(-2, 2, length.out = 1200),'+') %>% c()
opt <-  theme(legend.position="none",
panel.background = element_rect(fill="white"),
plot.margin=grid::unit(c(1,1,0,0), "mm"),
panel.grid=element_blank(),
axis.ticks=element_blank(),
axis.title=element_blank(),
axis.text=element_blank())
for (i in 1:35)
{
z=z0
# i iterations of f(z)
for (k in 1:i) z <- f(z, c=-0.621)
df=data.frame(x=Re(z0),
y=Im(z0),
z=as.vector(exp(-Mod(z)))) %>% na.omit()
p=ggplot(df, aes(x=x, y=y, color=z)) +
geom_tile() +
scale_x_continuous(expand=c(0,0))+
scale_y_continuous(expand=c(0,0))+
ggsave(plot=p, file=paste0("plot", stringr::str_pad(i, 4, pad = "0"),".png"), width = 1.2, height = 1.2)
}
# Place the exact path where ImageMagick is installed
system('"C:\\Program Files\\ImageMagick-6.9.3-Q16\\convert.exe" -delay 20 -loop 0 *.png julia.gif')
# cleaning up
file.remove(list.files(pattern=".png"))


# Zooming

You don’t have to be beautiful to turn me on (Kiss, Prince)

I discovered recently how easy is to create GIFs with R using ImageMagick and I feel like a kid with a new toy. To begin this new era of my life as R programmer I have done this:

First of all, read this article: it explains very well how to start doing GIFs from scratch. The one I have done is inspired in this previous post where I take a set of complex numbers to transform and color it using HSV technique. In this case I use this next transformation: f(z)= -Im(z)+(Re(z)+0.5*Im(z))*1i

Modifying the range of Real and Imaginary parts of complex numbers I obtain the zooming  effect. The code is very simple. Play with it changing the transformation or the animation options. Send me your creations, I would love to see them:

library(dplyr)
library(ggplot2)
dir.create("output")
setwd("output")
id=1 # label tO name plots
for (i in seq(from=320, to=20, length.out = 38)){
z=outer(seq(from = -i, to = i, length.out = 300),1i*seq(from = -i, to = i, length.out = 500),'+') %>% c()
z0=z
for (k in 1:100) z <- -Im(z)+(Re(z)+0.5*Im(z))*1i
df=data.frame(x=Re(z0),
y=Im(z0),
h=(Arg(z)<0)*1+Arg(z)/(2*pi),
s=(1+sin(2*pi*log(1+Mod(z))))/2,
v=(1+cos(2*pi*log(1+Mod(z))))/2) %>% mutate(col=hsv(h,s,v))
ggplot(df, aes(x, y)) +
geom_tile(fill=df$col)+ scale_x_continuous(expand=c(0,0))+ scale_y_continuous(expand=c(0,0))+ labs(x=NULL, y=NULL)+ theme(legend.position="none", panel.background = element_rect(fill="white"), plot.margin=grid::unit(c(1,1,0,0), "mm"), panel.grid=element_blank(), axis.ticks=element_blank(), axis.title=element_blank(), axis.text=element_blank()) ggsave(file=paste0("plot",stringr::str_pad(id, 4, pad = "0"),".png"), width = 1, height = 1) id=id+1 } system('"C:\\Program Files\\ImageMagick-6.9.3-Q16\\convert.exe" -delay 10 -loop 0 -duplicate 1,-2-1 *.png zooming.gif') # cleaning up file.remove(list.files(pattern=".png"))  # The Coaster Maker by Shiny The word you invented is well formed and could be used in the Italian language (The Accademia della Crusca regarding to the word “Petaloso”, recently invented by an eight-year-old boy) Are you tired of your old coasters? Do you like to make things by your own? Do you have a PC and a printer at home? If you answered yes to all these questions, just follow these simple instructions: • Install R and RStudio in your PC • Open RStudio and create a new Shiny Web App multiple file (ui.R/server.R) • Substitute sample code of each file by the code below • Press Run App • Press buttom Get your coaster! until you obtain a image you like • Print the image • Cut out the image • Place on the coaster your favorite drinking These are some examples: This is the code of ui.R # # This is the user-interface definition of a Shiny web application. You can # run the application by clicking 'Run App' above. # # Find out more about building applications with Shiny here: # # http://shiny.rstudio.com/ # library(shiny) shinyUI(fluidPage( titlePanel("The coaster maker"), sidebarLayout( sidebarPanel( #helpText(), # adding the new div tag to the sidebar tags$div(class="header", checked=NA,
tags$p("This coasters are generated by hypocycloid curves.The curve is formed by the locus of a point, attached to a circle, that rolls on the inside of another circle. In the curve's equation the first part denotes the relative position between the two circles, the second part denotes the rotation of the rolling circle.")), tags$div(class="header", checked=NA,
HTML("

),
),
mainPanel(
plotOutput("HarmPlot")
)
)
))


This is the code of server.R

# This is the server logic of a Shiny web application. You can run the
# application by clicking 'Run App' above.
#
# Find out more about building applications with Shiny here:
#
#    http://shiny.rstudio.com/
#
library(shiny)
library(ggplot2)
CreateDS = function ()
{
t=seq(-31*pi, 31*pi, 0.002)
a=sample(seq(from=1/31, to=29/31, by=2/31), 1)
b=runif(1, min = 1, max = 3)
data.frame(x=(1-a)*cos(a*t)+a*b*cos((1-a)*t), y=(1-a)*sin(a*t)-a*b*sin((1-a)*t))
}
shinyServer(function(input, output) {
dat<-reactive({if (input$rerun) dat=CreateDS() else dat=CreateDS()}) output$HarmPlot<-renderPlot({
ggplot(dat())+
geom_point(data=data.frame(x=0,y=0), aes(x,y), color=rgb(rbeta(1, .5, .5), rbeta(1, .5, .5), rbeta(1, .5, .5)) , shape=19, fill="yellow", size=220)+
geom_polygon(aes(x, y), fill=rgb(rbeta(1, 2, 2), rbeta(1, 2, 2), rbeta(1, 2, 2))) +
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())
}, height = 500, width = 500)
})


# Sunflowers

The world is full of wonderful things, like sunflowers (Machanguito, my islander friend)

Sunflower seeds are arranged following a mathematical pattern where golden ratio plays a starring role. There are tons of web sites explaining this amazing fact. In general, the arrangement of leaves on a plant stem are ruled by spirals. This fact is called phyllotaxis, and I did this experiment about it some time ago. Voronoi tessellation originated by points arranged according the golden angle spiral give rise to this sunflowers:

I know this drawing will like to my friend Machanguito because he loves sunflowers. He also loves dancing, chocolate cookies, music and swimming in the sea. Machanguito loves life, it is just that simple. He is also a big defender of renewable energy and writes down his thoughts on recycled papers. You can follow his adventures here.

This is the code:

library(deldir)
library(ggplot2)
library(dplyr)
opt = theme(legend.position  = "none",
panel.background = element_rect(fill="red4"),
axis.ticks       = element_blank(),
panel.grid       = element_blank(),
axis.title       = element_blank(),
axis.text        = element_blank())
CreateSunFlower <- function(nob=500, dx=0, dy=0) {   data.frame(r=sqrt(1:nob), t=(1:nob)*(3-sqrt(5))*pi) %>%
mutate(x=r*cos(t)+dx, y=r*sin(t)+dy)
}
g=seq(from=0, by = 45, length.out = 4)
jitter(g, amount=2) %>%
expand.grid(jitter(g, amount=2)) %>%
apply(1, function(x) CreateSunFlower(nob=round(jitter(220, factor=15)), dx=x[1], dy=x[2])) %>%
do.call("rbind", .) %>% deldir() %>% .$dirsgs -> sunflowers ggplot(sunflowers) + geom_segment(aes(x = x1, y = y1, xend = x2, yend = y2), color="greenyellow") + scale_x_continuous(expand=c(0,0))+ scale_y_continuous(expand=c(0,0))+ opt  # A Silky Drawing and a Tiny Experiment It is a capital mistake to theorize before one has data (Sherlock Holmes, A Scandal in Bohemia) One of my favorite entertainments is drawing things: crazy curves, imaginary flowerscelestial bodies, fractalic acacias … but sometimes I wonder myself if these drawings result interesting to whom arrive to my blog. One way to define interesting could be wanting to reproduce the drawing. I know some people do it because they sometimes share with me their creations. So, how many people appreciate the code I write? I manage some a priori for this number (which I will maintain for myself) but I want to refine my estimation with the next experiment. I have done this drawing, which shows that simple mathematics can produce very nice patterns: To estimate how many people is really interested in this plot, at the end of the post I will publish all the code except for a line. If you want the line, you will have to ask it to me. How? It is very easy: you will have to send me a direct message in Twitter. If you don’t follow me, do it here and I will follow you back. If you already follow me but I don’t, tweet something mentioning me and I will follow you back. Then you will be able to send me the direct message. If you prefer, you can send me an email. You can find my email address here. I know this experiment can be quite biased, but I am also pretty sure that the resulting estimation will be much better than the one I manage nowadays. This is the kidnapped code: library(magrittr) library(ggplot2) opt = theme(legend.position = "none", panel.background = element_rect(fill="violetred4"), axis.ticks = element_blank(), panel.grid = element_blank(), axis.title = element_blank(), axis.text = element_blank()) seq(from=-10, to=10, by = 0.05) %>% expand.grid(x=., y=.) %>% #HERE COMES THE KIDNAPPED LINE geom_point(alpha=.1, shape=20, size=1, color="white") + opt  # Going Bananas With Hilbert It seemed that everything is in ruins, and that all the basic mathematical concepts have lost their meaning (Naum Vilenkin, Russian mathematician, regarding to the discovery of Peano’s curve) Giuseppe Peano found in 1890 a way to draw a curve in the plane that filled the entire space: just a simple line covering completely a two dimensional plane. Its discovery meant a big earthquake in the traditional structure of mathematics. Peano’s curve was the first but not the last: one of these space-filling curves was discovered by Hilbert and takes his name. It is really beautiful: Hilbert’s curve can be created iteratively. These are the first six iterations of its construction: As you will see below, R code to create Hilbert’s curve is extremely easy. It is also very easy to play with the curve, altering the order in which points are sorted. Changing the initial matrix(1) by some other number, resulting curves are quite appealing: Let’s go futher. Changing ggplot geometry from geom_path to geom_polygon generate some crazy pseudo-tessellations: And what if you change the matrix exponent? And what if you apply polar coordinates? We started with a simple line and with some small changes we have created fantastical images. And all these things only using black and white. Do you want to add some colors? Try with the following code (if you draw something interesting, please let me know): library(reshape2) library(dplyr) library(ggplot2) opt=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()) hilbert = function(m,n,r) { for (i in 1:n) { tmp=cbind(t(m), m+nrow(m)^2) m=rbind(tmp, (2*nrow(m))^r-tmp[nrow(m):1,]+1) } melt(m) %>% plyr::rename(c("Var1" = "x", "Var2" = "y", "value"="order")) %>% arrange(order)} # Original ggplot(hilbert(m=matrix(1), n=1, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(1), n=2, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(1), n=3, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(1), n=4, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(1), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(1), n=6, r=2), aes(x, y)) + geom_path()+ opt # Changing order ggplot(hilbert(m=matrix(.5), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(0), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(tan(1)), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(3), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(-1), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(log(.1)), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(-15), n=5, r=2), aes(x, y)) + geom_path()+ opt ggplot(hilbert(m=matrix(-0.001), n=5, r=2), aes(x, y)) + geom_path()+ opt # Polygons ggplot(hilbert(m=matrix(log(1)), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(.5), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(tan(1)), n=5, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-15), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-25), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(0), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(1000000), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-1), n=4, r=2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-.00001), n=4, r=2), aes(x, y)) + geom_polygon()+ opt # Changing exponent gplot(hilbert(m=matrix(log(1)), n=4, r=-1), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(.5), n=4, r=-2), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(tan(1)), n=4, r=6), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-15), n=3, r=sin(2)), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-25), n=4, r=-.0001), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(0), n=4, r=200), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(1000000), n=3, r=.5), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-1), n=4, r=sqrt(2)), aes(x, y)) + geom_polygon()+ opt ggplot(hilbert(m=matrix(-.00001), n=4, r=52), aes(x, y)) + geom_polygon()+ opt # Polar coordinates ggplot(hilbert(m=matrix(1), n=4, r=2), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(-1), n=5, r=2), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(.1), n=2, r=.5), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(1000000), n=2, r=.1), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(.25), n=3, r=3), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(tan(1)), n=5, r=1), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(1), n=4, r=1), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(log(1)), n=3, r=sin(2)), aes(x, y)) + geom_polygon()+ coord_polar()+opt ggplot(hilbert(m=matrix(-.0001), n=4, r=25), aes(x, y)) + geom_polygon()+ coord_polar()+opt  # Phyllotaxis By Shiny 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 )}
)