Code to reproduce https://mbq.me/blog/nomads/

nom2.brew.svg

nom3.brew.svg

nomads-make-all.R

source('nomads.R');

library(ggplot2);
library(brew);

#Run simulationA, but only once
if(!exists("simA"))
 simulationA()->simA;

#Plot
ptA<-ggplot(simA,aes(y=Distance,fill=Solution,x=p))+
 geom_hline(yintercept=1/7)+
 geom_boxplot(outlier.size=NA)+
 theme(legend.position="bottom");
print(ptA);

#Make SVG animations
brew('nom2.brew.svg','nom2.svg');
brew('nom3.brew.svg','nom3.svg');

nomads.R

#Generate votes, as complex numbers
generateVotes<-function(N=500,p=0.3)
 exp(1i*ifelse(p<runif(N),
  runif(N,0,2*pi), #Those who have no idea
  rnorm(N,0,5/180*pi)  #Those who know, with a small deviation of sd=5deg
 ))

distance<-function(z)
 abs(z-(1+0i))

vote<-function(z){
 sum(z)->z
 return(z/abs(z))
}

baselineDistance<-function(trials=1000,...)
 distance(exp(1i*runif(trials,0,2*pi)))

singleDistance<-function(trials=1000,p=0.3,...)
 distance(sample(generateVotes(N=trials,p)))

ensembleDistance<-function(trials=1000,N=500,p=0.3,...)
 replicate(trials,distance(vote(generateVotes(N,p))))

#Make simulation
simulationA<-function(trials=10000,p=c(.01,.03,.05,.1,.3,.5,.7,.75,.8)){
 BD<-data.frame(
  p=0,
  Solution="Random direction",
  Distance=baselineDistance(trials)
 );
 RD<-do.call(rbind,lapply(p,function(p)
  data.frame(
   p=p,
   Solution="Single nomad",
   Distance=singleDistance(trials,p)
  )
 ));
 VD500<-do.call(rbind,lapply(p,function(p)
  data.frame(
   p=p,
   Solution="Ensemble voting 500",
   Distance=ensembleDistance(trials,500,p)
  )
 ));
 VD5k<-do.call(rbind,lapply(p,function(p)
  data.frame(
   p=p,
   Solution="Ensemble voting 5k",
   Distance=ensembleDistance(trials,5000,p)
  )
 ));
 rbind(BD,RD,VD500,VD5k)->U;
 U$p<-factor(U$p);
 U
}

#Generate "hedgehog" plots as SVG paths, for nom2.brew.svg
genPath<-function(z,r=90)
 paste(sprintf("M0,0L%0.1f,%0.1f",r*Re(z),r*Im(z)),collapse="")

genPaths<-function(N=50,p=0.01){
 ans<-list();

 exp(1i*runif(floor(N*(1-p)),0,2*pi))->ans$guessing;
 exp(1i*rnorm(ceiling(N*p),0,5/180*pi))->ans$knowing;

 #Voting result
 sum(c(ans$guessing,ans$knowing))->vote;

 #Vector averages of both, normalised
 sum(ans$guessing)/abs(vote)->ans$ave_guess;
 sum(ans$knowing)/abs(vote)->ans$ave_know;

 #Final, normalised direction
 vote/abs(vote)->ans$vote;

 lapply(ans,genPath)
}

genPathsCelebrity<-function(N=50,p=0.01){
 ans<-list();

 exp(1i*rnorm(floor(N*(1-p)),runif(1,0,2*pi),1.5))->ans$guessing;
 exp(1i*rnorm(ceiling(N*p),0,5/180*pi))->ans$knowing;

 #Voting result
 sum(c(ans$guessing,ans$knowing))->vote;

 #Vector averages of both, normalised
 sum(ans$guessing)/abs(vote)->ans$ave_guess;
 sum(ans$knowing)/abs(vote)->ans$ave_know;

 #Final, normalised direction
 vote/abs(vote)->ans$vote;

 lapply(ans,genPath)
}