Scale numbers to be <= 255?

Question

I have cells for whom the numeric value can be anything between 0 and Integer.MAX_VALUE. I would like to color code these cells correspondingly.

If the val

Answer 1

I figured a log fit would be good for this, but looking at the results, I'm not so sure.

However, Wolfram|Alpha is great for experimenting with this sort of thing:

I started with that, and ended up with:

r(x) = floor(((11.5553 * log(14.4266 * (x + 1.0))) - 30.8419) / 0.9687)

Interestingly, it turns out that this gives nearly identical results to Artelius's answer of:

r(x) = floor(255 * log(x + 1) / log(2^31 + 1)

IMHO, you'd be best served with a split function for 0-10000 and 10000-2^31.