Another of those things I would get around to, some day.. but I did!
Every y-value is the result of iterating x[next] = rx(1-x); (where r is the point on the x-axis and x is a random seed, 0.5 in this case) until it stabilizes or falls into a repeating pattern. source, info, related.
For the scale: the graph starts at 2.4, splits the first time at 3, ends at 4, and is 1 high. The red line is what would usually be the x-axis.