##################################################################################
# MULTIPLE SCALES MAY BE PERTINENT FOR THE STUDY OF SPATIAL PATTERN
##################################################################################

# define space
x <- seq(1,100,0.1)

# define four components of a spatial pattern
y1 <- sin(x/15)
y2 <- sin(x/10)
y3 <- sin(x/5)
y4 <- sin(x)

# plot the components
plot(x, y1, type="l", lwd=4)
plot(x, y2, type="l", lwd=4)
plot(x, y3, type="l", lwd=4) 
plot(x, y4, type="l", lwd=4)

# create matrix with the four compoenents of the spatial pattern
ev <- cbind(y1,y2,y3,y4)
summary(ev)
var(ev)
sev<-scale(ev)
summary(sev)
var(sev)
attributes(sev)

# plot combinations of the components of the spatial pattern
plot((sev[,1] + sev[,2]), type="l", lwd=5)
points(sev[,1], col="red")
points(sev[,2], col="blue")

plot(sev[,1] + sev[,3], type="l", lwd=5)
points(sev[,1], col="red")
points(sev[,3], col="blue")

plot(sev[,1] + sev[,4], type="l", lwd=5)
points(sev[,1], col="red")
points(sev[,4], col="blue")

plot(sev[,2] + sev[,3], type="l", lwd=5)
points(sev[,2], col="red")
points(sev[,3], col="blue")

plot(sev[,2] + sev[,4], type="l", lwd=5)
points(sev[,2], col="red")
points(sev[,4], col="blue")

plot(sev[,3] + sev[,4], type="l", lwd=5)
points(sev[,3], col="red")
points(sev[,4], col="blue")