Displaying fine variation across multiple orders of magnitude I have a sequence of numbers that grows super-exponentially:
0.993, 0.999, 1.037, 1.054, 1.195, 1.55, 2.953, 15.369, 815.687, 26492.118

I'd like to be able to plot the data in such a way that the viewer will be able to tell how the whole sequence increases: for my application, the first few values are especially important, but I'd still like to show the whole range.  So I tried a log scale (which stretches out small values), but the first five values still look pretty indistinguishable.
I could take the log twice, but that would probably hurt interpretability and I couldn't display the two values that were less than one (because they'd be negative after the first log transformation).
Right now I'm thinking about splitting it into two plots with different Y axes, but I thought I'd see what the community suggested.  Thanks in advance for your time.
 A: Your idea of two plots with different scales is better than a broken axis since it gives you a perceptual view of how disparate the values are. Below is a quick mock-up. For presentation, the two graphs should have more separation and some cue or text that one is a zoomed in view of the other.

Log or some other transformation may still be best to show the power of the growth. Here's log.

Another option is to plot some derived value, such as the ratio yk+1/yk.
A: Let's step back, and think how to represent data instead of how to visualize data. I love data visualization but I'd say that graph is not a suitable solution here.
Let's evaluate your requests:

  
*
  
*I'd like to be able to plot the data in such a way that the viewer will be able to tell how the whole sequence increases
  
*[F]or my application, the first few values are especially important, but I'd still like to show the whole range.
  

The problem with graphs with original or log scale is that it's still practically impossible to name the first few values from those graphs, which is your objective #2.
A graph is on the only tool to show range, you can also tabulate your readings:
    0.993
    0.999
    1.037
    1.054
    1.195
    1.550
    2.953
   15.369
  815.687
26492.118

Most people can immediately notice that very high rate of growth, which should fulfill your objective #1. In the mean time, you got to keep the true data of the first few cases. And if you so wish, you can even plot those first few cases using the original scale.
