phi.r

fnums <- c(1, 1)
x <- 1:30
phi <- c()
pdiff <- c()

actual = 0.5 * (1 + 5^0.5)

for (i in x) {
	next_fibo = fnums[i] + fnums[i+1]
	fnums <- c(fnums, next_fibo)
	
	approx = fnums[i+1] / fnums[i]
	phi <- c(phi, approx)
	
	difference = abs((approx - actual)/actual * 100)
	pdiff <- c(pdiff, log(difference))
}

par(mfrow=c(2,1))

plot(x, phi, type = "l", col = "red", lwd = 3, ylab="Approximate value of phi", xlab="Number of points")
plot(x, pdiff, pch=16, ylab="Log10 of % Difference", xlab="Number of points")
abline(lm(x ~ pdiff))