Hypnotical Fermat

December 1, 2015
By

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Se le nota en la voz, por dentro es de colores (Si te vas, Extremoduro)

This is a gif generated with 25 plots of the Fermat’s spiral, a parabolic curve generated through the next expression:

r^{^2}= a^{2}\Theta

where r is the radius, \Theta is the polar angle and a is simply a compress constant.

Fermat showed this nice spiral in 1636 in a manuscript called Ad locos planos et solidos Isagoge (I love the title). Instead using paths, I use a polygon geometry to obtain bullseye style plots:
FermatGIF
Playing with this spiral is quite addictive. Try to change colors, rotate, change geometry … You can easily discover cool images like this without any effort:
Fermat065
Enjoy!

library(ggplot2)
library(magrittr)
setwd("YOUR-WORKING-DIRECTORY-HERE")
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())
for (n in 1:25){
t=seq(from=0, to=n*pi, length.out=500*n)
data.frame(x= t^(1/2)*cos(t), y= t^(1/2)*sin(t)) %>% rbind(-.) -> df
p=ggplot(df, aes(x, y))+geom_polygon()+
scale_x_continuous(expand=c(0,0), limits=c(-9, 9))+
scale_y_continuous(expand=c(0,0), limits=c(-9, 9))+opt
ggsave(filename=paste0("Fermat",sprintf("%03d", n),".jpg"), plot=p, width=3, height=3)}

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