Entropy Filter v4

It occurred to me several weeks ago that my ad-hoc entropy filter would better mirror the entropy equations if I too the log of the sum instead of the sum of logs. I made a Intensity/Entropy scattergram using this modification.

The result is very similar to the previous one, but there seems to be an interesting feature in the new plot.

What is that line near the top of the scattergram?

I really need create a way to map areas of these plots back to pixels.

The Problem with a Fair Coin

It has been a while since I have posted. Last time, I was working on Elements of Information Theory before I had to return it to the library.

I didn't get very far (and it has been nearly a month since I returned it).

My main approach with technical book is to implement solutions to the end of chapter problems in software. The first question in this book is as follows:

A fair coin is flipped until the first head occurs. Let X denote the number of flips required. Find the entropy H(X) in bits.

This is a fairly easy problem to solve (especially with the series summation provided with the question). However, the solution has a very high barrier in software.

To write a general software solution, I would need the following:
1) Representation of sums of infinite series.
2) Ability to convert a random variable description into the infinite series.
3) Ability to manipulate the infinite series until it matches a function with a known closed form solution.

Once I've gotten to that point, the use of the closed form solution isn't very useful.

I tend to get stuck chasing rabbit holes like this. I didn't make much progress after I got stuck in this tar pit.

The book is back at the library now and I'm going to head back to my vision work.