Most of us own a digital camera; most likely you have a couple of them (plus a smartphone or two that takes pictures!) Over the last couple of years you’ve probably accumulated hundreds, or possibly thousands, of digital photographs.

IMG_0123.JPG and IMG_0124.JPG do these names sound familiar?*

By default, digital cameras start off with a base filename and increment a post-pended number with each exposure.

*Another popular prefix is DSC and your hard drive might be full of images that look like DSC_0123.JPG

If you’re like me, you never bother to change any of your camera parameters; you simply snap-away then drag-n-drop the files off to your computer for storage and/or to the cloud. (Typically at random intervals, or maybe at the end of a vacation or trip).

Even after I’ve download images to my computer, I very rarely rename any of the files, so my computer has many duplicated image filenames.

When you purchase a new camera, images typically start being recorded with the filename IMG_0001.JPG and increase from there.

I was curious if other people did a similar lazy thing, so this afternoon I did a quick search on flickr for usage of filenames in the format IMG_XXXX.JPG There are quite a lot of them!

It seems that even semi-professionals and passionate amateurs don’t often rename their submissions.

Then, I became more curious about the distribution of filenames.

How many are labeled IMG_0001.JPG how many are labeled IMG_0002.JPG … ?

Do people upload all their photos, or just their ‘good’ ones?

If they upload all of them, then the quantity of photos per filename should decrease as the filenumber increases – If there is no IMG_0099.JPG then there will not be an IMG_0100.JPG from the same upload).

Working against this is the fact that, whilst many cameras reset their filenumber back to 0000 after transfer, many have the option to make the current filenumber the programming equivalent of a STATIC variable and remember it even after the current images are transferred and removed (so only rolling around and repeating filenames after 10,000 images have been taken).

(I've included close-ups of each glitch below, and highlighted them on the right)

The first glitch occurs at IMG_0532.

I'm stumped as to the cause of this one. I can think of nothing significant about this number, and why photographs with this filenumber occur with a frequency 30% higher than numbers directly either side! Outside of some indexing issue on the flickr server I'm at a loss. If anyone knows (or would like to speculate a reason), drop me an email and I'll be happy update this article.  UPDATE - See end of article 

The next glitch occurs at IMG_1000 where there is a slight fall. As this number is a round number I can speculate that people might want to rename this particular file. It's a much smaller glitch than the previous, being just an 8% deviation from the curve.

Logarithmic decay is fascinating in that it appears far less often in analysis than its well-known cousin the exponential decay.

Many physical parameters decay in a mathematically exponential way because of the nature of the situation.

Exponential decay models, in a simple form, the concept of survivability, where a certain number of items exist and there is a probability of each element decaying at each time interval, leaving less from that point on.

In logarithmic decay, there is an initial rapid decline, then a slowing of the rate. One other example of a logarithmic function is Benford's Law, which I wrote about earlier this year.

If you think about it, the number of photographs with a particular filenumber is not a function of decay from previous filenumbers like some form of radioactive decay (which exponential decay would model). Instead it’s an additive representation of a superposition of ordered ranges of numbers. Let me explain more with a thought experiment …

I like to take pictures of my family, but I don't have over 10,000! Digital cameras have certainly changed the way we, as a society, capture photographs. In the ‘old’ world of print film, care was taken to plan out a shot as the costs of production (both in terms of development costs and processing time) were large. Each roll of film typically had 36 exposures, so albumns were limited in size. These days, digital memory cards and storage costs are so low (and of such high capacity) that collection and compilation is only limited by your patience!