# Hypnotical Fermat

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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:

where is the radius, is the polar angle and 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:

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:

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)}

To

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