R code inspired by prompt 3 of genuary 2025 "Exactly 42 lines of code"

fortytwo.r

N=42
ratio=0.8
t = seq(1,N/2*pi,l=100000)
stepper = .5*(2*((t%%pi)/pi-0.5))^5 + (t%/%pi)
circle = function(a,p,f) {
  exp(1i*(t*f + p + 0*t/N*.5))*a
  }
w=1000
Nf=N/6
drawchar = function(x,y,width,height,a=1,p,f,...){
  a1 = rep(sample(1:N)/N, each=length(t)/N) 
  a1 = zoo::rollmean(a1,w,fill=c(a1[1],NA, tail(a1)[1]))
  a2 = rep(sample(1:N)/N, each=length(t)/N) 
  a2 = zoo::rollmean(a2,w,fill=c(a2[1],NA, tail(a2)[1]))
  a3 = rep(sample(1:N)/N, each=length(t)/N) 
  a3 = zoo::rollmean(a3,w,fill=c(a3[1],NA, tail(a3)[1]))
  f3 = rep(sample(-5:5,Nf,TRUE), each=length(t)/Nf) 
  f3 = zoo::rollmean(f3,1,fill=c(f3[1],NA, tail(f3)[1]))
  f2 = rep(sample(-5:5,Nf,TRUE), each=length(t)/Nf) 
  f2 = zoo::rollmean(f2,1,fill=c(f2[1],NA, tail(f2)[1]))
  f1 = rep(sample(-5:5,Nf,TRUE), each=length(t)/Nf) 
  f1 = zoo::rollmean(f1,1,fill=c(f1[1],NA, tail(f1)[1]))
  z=(circle(a,p[1],f[1]) + circle(a1,p[2],f1)+ circle(a2,p[3],f2)+ circle(a3,p[4],f3))
  z2=1+x+1i*y+ 2*stepper+ .5*width*Re(z) + 
           1i*width*(Im(z)-min(Im(z))-1i*min(Im(z)))/(max(Im(z))-min(Im(z)))
  points(z2[1:(length(z2)*ratio)],...) 
}
res=4000
png("fortytwolines.png",width=res*ratio,height=res,type="cairo")
par(bg="#ddeeff",col="blue",mar=10*c(1,1,1,1))
plot(NA,xlim=(c(-N/2,N/2*(1-(2*(1-ratio))))),ylim=c(0,N)+.1,asp=1,ann=FALSE,axes=FALSE)
for(i in 0:(N)) abline(h=i-0.5,lty="dotted",lwd=3)
for(i in 0:(ratio*N+1)) abline(v=i-0.5-N/2,lty="dotted",lwd=3)
for(i in 1:N){
    drawchar(-N/2+.1,i+.1-1,width = ratio,01,
             p=c(0,pi/2,2*pi*runif(2)),
             f=sample(-5:5,4,TRUE),
             pch=19,
             cex=runif(10000)^4,
             col=hsv(.6,.2,.1,0.05))
}
dev.off()