The following code produces an image:
library(latticeExtra)
x=runif(40)
y=runif(40)
z=runif(40)
png(filename=paste(i,".png",sep=""))
levelplot(z ~ x + y, panel = panel.levelplot.points, col.regions = rainbow(50))
dev.off()
But the following code does not. Why?
library(latticeExtra)
for(i in seq(1,5)) {
    x=runif(40)
    y=runif(40)
    z=runif(40)
    png(filename=paste(i,".png",sep=""))
    levelplot(z ~ x + y, panel = panel.levelplot.points, col.regions = rainbow(50))
    dev.off()
}
                Well, I'll just write what I wrote in the comments as an answer.
When plotting lattice or ggplot2 plots inside your own loops or functions, you have to explicitly print the lattice/ggplot2 plots
Try this:
library(latticeExtra)
png(filename="plot_%02d.png")
for(i in seq(1,5)) {
    x=runif(40)
    y=runif(40)
    z=runif(40)
    # Assign your lattice plot to myPlot
    myPlot <- levelplot(z ~ x + y, panel = panel.levelplot.points, col.regions = rainbow(50))
    print(myPlot)
}
dev.off()
I believe this part of the R FAQs is relevant here: 7.22 Why do lattice/trellis graphics not work?
EDIT:
I changed the png code to come before the loop and placed dev.off() outside of the loop.
png(filename="plot_%02d.png") will save the first plot as plot_01.png, the second plot as plot_02.png, etc.
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