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:

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 functionattractor = 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 galaxyz1=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 galaxyz2=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 galaxyz3=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 galaxyz4=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