Reverse Fractal Sock Theory

First, take however many pairs of socks you need [in this case, a lot]. Call this number 's'. Now, put them in an [improbably large] house where the number of people = s/2. Now, number each of the pairs 1,2,3... s, and at the same time, make a graph where the x axis also goes 1,2,3... s, and where the y axis goes week 1, week 2, week 3 etc.

Leave for a week, while the people get on with their normal, sock- wearing lives.

When you return, gather all the socks that are still wearable [it doesn't matter if they're dirty or being washed, but don't count ones that are too full of to wear] and findable. Once a sock is declared 'lost', don't attempt to look for it.

Put the socks back into pairs, and count them again. For every pair that is still intact, draw a vertical line to the 'week 1' line.

Now, unless the sockkeeping in the house is exceptional, you should be left with some odd socks. Take the first number which has only one sock, and take the second. Find the midpoint between the two, and mark it on the 'week 1' line. Now, draw a straight line to link each of the 'single-sock' numbers to the mark. These 2 socks are now combined as a pair, and will be till one or other is lost/destroyed.

If there is an odd one left at the end, draw a line that links it to the edge of the graph, but still level with the 'week 1' line.

For any numbers where both socks are missing, draw no line.

Repeat this process for however many weeks it takes [probably surprisingly few] to get down to just one single pair of socks. If you then look at the graph, it [hopefully] produces a reverse fractal pattern, culminating in one single line that is the last pair of socks.