Figure 9.1 from Statistical Rethinking (bottom-right plot)

entropy_as_logways.R

p <- list()
p$A <- c(0,0,10,0,0)
p$B <- c(0,1,8,1,0)
p$C <- c(0,2,6,2,0)
p$D <- c(1,2,4,2,1)
p$E <- c(2,2,2,2,2)

p_norm <- lapply( p , function(q) q/sum(q))
( H <- sapply( p_norm , function(q) -sum(ifelse(q==0,0,q*log(q))) ) )

W <- function(n,N) factorial(N)/prod(factorial(n))
ways <- sapply( p , W , N=10 )
logwayspp <- log(ways)/10

plot(logwayspp,H,xlab="log(ways) per pebble",ylab="entropy",pch=16)
abline(lm(H~logwayspp),lty=2,col=col.alpha("black",0.5))
text( logwayspp , H , labels=c("A","B","C","D","E") , cex=1.1 , 
    pos=c(3,3,1,1,1) )