A fractal in the real world

Of course, real world fractals do exist, but it is interesting to appear to have “discovered” one, or at least a pattern which certainly shows many fractal-like properties.

I am plotting the relative efficiency of different page replacement algorithms – and here I am looking at Belady’s OPT (or MIN), or as it is sometimes called, the clairvoyant page replacement algorithm.

Here I am measuring the proportion of time a page stands idle (including its loading time). So a page with a ratio of 1.0 is loaded but never used, a page with a ratio of 0.999 is used one-thousandth of the time it is in the system and a page with a ratio of 0.99 is used one-hundredth of the time it’s in the system and so on.

So, here’s the “full” plot for my data:

Full OPT plot

Not much to see – except most pages are idle most of the time: so we go closer:


And closer…


And closer…


That’s about the limit of the precision of the data, but it looks pretty fractal like to me…

(Should add, other page replacement policies studied don’t appear to show this fractal-like pattern, exhibiting only one peak/modal frequency.)