Thread: Zipf's Law

So, infrastructure evolves just as creatures do--through natural selection. It also follows logic that we'd converge methods, as well (noting the lung=plumbing example).

Relevant to my interests.

That's pretty neat. I took the liberty of graphing this in Excel for we visual folks:

As you can see, the top 25 US cities adhere pretty closely to Zipf's Law, although the actual populations overshoot the predicted populations pretty consistently (albeit not by much). Apparently our largest city needs to be a little bit bigger in order to put it all back into proportion.

Nice work on the graph! Zipf's law seems to hold consistently for the top 4 or 5, after which it seems like there are tiers or clusters, with 2 or 3 cities at the same level. Of course, deciding where to draw the line on a metro area is fuzzy these days, too, rendering the population numbers iffy.

I wonder if this has some connection to a sort of critical mass effect. Once a city is known as 'the largest', all of a sudden twice as many people want to live there sort of thing.

Hah, interesting. Good article about it on Wikipedia:

http://en.wikipedia.org/wiki/Zipf%27s_law

Check out the log log graph for word frequencies.

Apparently it also applies to random strings of words so it could just be an artefact... cool though.

This only seems to hold true for America. Looking at the other 3 of the top 4 most populous nations:

China:

1. Shanghai - 18,580,000
2. Beijing - 12,133,000
3. Guangzhou - 10,045,800
4. Shenzhen - 8,464,300
5. Xianggang (Hong Kong) - 7,000,000

India:

1. Mumbai - 13,922,125
2. Delhi - 12,259,230
3. Bangalore - 5,310,318
4. Kolkata (Calcutta) - 5,080,519
5. Chennai - 4,590,267

Indonesia:

1. Jakarta - 10,810,400
2. Bandung - 2,884,300
3. Surabaya - 2,729,300
4. Medan - 2,059,300
5. Bekasi - 1,994,850