Tag Archives: Butterfly Curve

A Little Present For Coldplay

Drawings, , , , ,

Gravity, release me, and don’t ever hold me down, now my feet won’t touch the ground (Coldplay, Life In Technicolor II)

Inspired by this nice post and by this cover of a Coldplay’s album:

20090515-coldplay1

I have dared to do this using ggplot, polar coordinates and Google Fonts:

coldplay

Coldplay: feel free to use it for some future album.

library(ggplot2)
library(extrafont)
windowsFonts(Monoton=windowsFont("Monoton"))
butterfly=function(x) 8-sin(x)+2*sin(3*x)+2*sin(5*x)-sin(7*x)+3*cos(2*x)-2*cos(4*x)
opt=theme(legend.position="none",
          panel.background = element_rect(fill="black"),
          panel.grid = element_blank(),
          axis.ticks=element_blank(),
          axis.title=element_blank(),
          axis.text =element_blank())
ggplot(data.frame(x = c(0, 2*pi)), aes(x)) +
  stat_function(fun=butterfly, geom="density", fill="#FC0C54", colour="#FC0C54") +
  coord_polar(start=-pi)+
  geom_text(x=.5, y=-14, colour="turquoise2", family="Monoton", label="COLDPLAY", size=12)+
  geom_text(x=1.5, y=14, colour="turquoise2", family="Monoton", angle=90, label="Up Down Up Down Up Down", size=6)+
  opt

butteRfly

Image Processing, , , ,

Float like a butterfly, sting like a bee (Muhammad Ali)

The Butterfly Curve was discovered by Temple H. Fay when he was in Southern University, Mississippi, and rapidly gained the attention of students and mathematicians because of its beautiful simmetry. Small dots of this plot are generated according to parametric equations of the Butterfly Curve. Big dots are randomdly distributed over the canvas:

butterfly4

This is the code to create butterflies:

library(ggplot2)
npoints=500
npointsb=1200
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())
t=seq(0,10*pi,length=npointsb)
butterfly=data.frame(x=sin(t)*(exp(1)^cos(t)-2*cos(4*t)-(sin(t/12))^5), y=cos(t)*(exp(1)^cos(t)-2*cos(4*t)-(sin(t/12))^5), s=runif(npointsb, min=.1, max=10), f=factor(sample(1:10,npointsb,TRUE)), a=runif(npointsb,min=.1, max=.4))
points=data.frame(x=runif(npoints,-4,4), y=runif(npoints,-3,5), s=runif(npoints,min=30, max=50), f=factor(sample(1:10,npoints,TRUE)), a=runif(npoints,min=.05, max=.15))
data=rbind(butterfly, points)
ggplot(data, aes(x, y, colour=f))+geom_point(alpha=data$a,size=data$s)+opt