# Plotting distributions of variables across time

I have two datasets in the form of $q \times k$ matrices (variables $x$ and $y$). Both variables differ (lets assume that they differ by a constant). Columns of the matrices are subsequent points in time, rows are observations (sample quantiles). The problem is to visualize those two variables to show differences between them and their variances across the time. The raw data is available. Plot needs to be readable to lay persons.

Below I paste the synthetic data that can serve as illustration.

set.seed(123)
mu <- 0
n <- 1000
k <- 10
q <- 10
x <- matrix(NA, q, k)
y <- matrix(NA, q, k)

for (i in 1:k) {
x[, i] <- quantile(rnorm(n, mu[i], 1), c(seq(0, 1, by=.1)-.05)[-1])
y[, i] <- quantile(rnorm(n, mu[i]+1.5, 1), c(seq(0, 1, by=.1)-.05)[-1])
mu[i+1] <- mu[i] + runif(1, -1, 1)
}


Do you have any ideas how could it be visualized? Let's take $x$ first. Use the quantiles to construct a smooth distribution $x_j(\cdot)$ at each timestep $j$. Pick a 1D grid of values $a + bi$. Now plot the greyscale image $x_j(a+bi)$, where $i$ is the row coordinate and $j$ is the column coordinate, and the $x$-values are normalized to 0-255.
Now do the same for $y$, and put the plots one above the other. If you'd prefer to combine them, then plot $x$ in the red channel and $y$ in the blue. If you do that though, do some reading on the perception of color first. Rainbow Color Map (Still) Considered Harmful is a nice summary of the problems you can encounter.