# Playing With Julia (Set)

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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) setwd("YOUR WORKING DIRECTORY HERE") 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))+ scale_colour_gradientn(colours=brewer.pal(8, "Paired")) + opt 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"))

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