I have been trynig to read Fractal geometry since the start of this year(perhaps a couple of months earlier). Have been too lazy/distracted, but manage to pick it up about once a month or so.
I picked up the Fractal geometry book again, went through the basics of measure theory(which is where i was the last time i picked it up). First thought ok let’s apply these prerequisites for measures to measures, you already know are being used and see if they obey the conditions. (Length,weight both apply. ok now find something from s/w engg. you are a programmer not a physicist) Lines of code(LOC). Ok it obeys all three rules.
1.$ measure of null set == 0
2. measure of A1 >= measure of A2 if A2 is a subset of A1
3. measure of union of A1,A2,A3….An == sum of measures of A1,A2,A3…An
Now the lines of code metric does obey all these rules, i can see why it appeals to so many people. The hidden trick, the last rule gets tricky. how do you account for builtin libraries and their lines of code?? Then it struck me, you can get different LOC by calling some libraries builtin and not Lines of code. and more importantly, in terms of functions(not just code,but feature sets, or as in function point analysis,) the LOC varies. it all comes down to what level of abstraction you choose for your functions. And in that sense, sometimes programs can have a fractional dimension. And exactly in that sense programs are fractals. That means there needs to be level of self-similarity within a program/software. And the best programs/sw are the ones that have some self-similarity but also provide rich variations like Julia and Mandelbrot set as opposed to Serpinski triangle or cantor set.