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Introduction
I got interested in layered sedimentation from viewing a video and decided it would be interesting to code this into R. More on that in due course, but my first step was to code a syatem with one sediment “type”.
Procedure
The following code drops sediment particles at x=1, and lets them roll downhill
until they reach the bottom or a ledge. It draws numbers at the sedimented
particles’ final positions. Since the numbers start at 1, the values are like
inverse ages.

m < 51 # number of particles
n < 10 # grid width
debug < FALSE # put TRUE for debugging
info < function(...) if (debug) cat(...)
pch < 20
cex < 4/log2(n)
type < "t"
set.seed(1)
rollDownhill < function(X, Z) {
info("rollDownhill(", X, ",", Z, ")\n", sep = "")
if (Z == 1)
return(list(x = X, z = Z))
## Particles roll downslope until they hit the bottom... ... or a ledge
## comprising two particles.
XX < X
ZZ < Z
while (0 == S[XX + 1, ZZ  1]) {
# move down and to right
info(" XX:", XX, " ZZ:", ZZ, "\n")
XX < XX + 1
ZZ < which(0 == S[XX, ])[1]
if (ZZ == 1)
break
if (XX == n)
break
}
return(list(x = XX, z = ZZ))
}
S < matrix(0, nrow = n, ncol = n) # 'S' means 'space'
par(mar = c(3, 3, 1, 1), mgp = c(2, 0.7, 0))
plot(1:n, 1:n, type = "n", xlab = "", ylab = "")
xDrop < 1 # location of drop; everything goes here or to right
for (i in 1:m) {
# 'p' means partcle
while (0 == length(zDrop < which(0 == S[xDrop, ])[1])) {
info("in while line 72\n")
xDrop < xDrop + 1
if (xDrop == n) {
message("RHS")
break
}
}
info("particle:", i, " ")
p < rollDownhill(xDrop, zDrop)
S[p$x, p$z] < 1
if (type == "p") {
points(p$x, p$z, col = "gray", pch = pch, cex = cex)
} else {
text(p$x, p$z, i, col = "gray")
}
}

Discussion and conclusions
Reading the numbers on the graph as inverse age, one can see an interesting age
structure.
Viewed along diagonals, ages increase by 1 time unit with every lateral step
away from the source.
Viewed along Z levels, though, the time step is more interesting. You can see
this at a glance, by firstdifferencing the values along z=1, and then at z=2,
etc.
I suppose that if something came along and sliced the sediment mound along z
levels, we’d see this more interesting pattern of time variation in the
lateral.
I wonder if these patterns (or the code) are of interest to geologists?
Resources
 Source code: 20140608slumpingmodel.R
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