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Of course the biggest shortcoming of all is that breeding will quickly outpace the food supply and many cats will starve to death or die of other causes without having reproduced.
Realistically, sure, but if someone were really determined to carry this out in real life - let's say, the government of Thailand for no real reason - they'd be able to afford to feed 10,000 cats pretty easily.

Oh, and what if we assume that the cats can or will eat each other, or corpses of other cats?

Thing is this: 1) not all survive out of a litter, even after several weeks, 2) if a cat has litters too close together, she will often refuse to nurse the second litter and they will all die. If everything that gave birth by litter survived, we humans wouldn't be here.
Right, so cats are close to an r-selection strategy:

http://en.wikipedia.org/wiki/R/K_selection_theory

If you were to do the same calculation with fruit flies, or even bacteria, you'd probably reach the number of atoms in the universe (~ 10^80) in less than five years. For various reasons, the exponential will turn into a logistic curve pretty soon (unstated assumptions of the article include the availability of food, water, space and the absence of predators).

It is possible to have dozens or more, since the female cat can have a litter from multiple sires. A female cat can mate with multiple tom's during the estrus (7-21 days) or heat cycle.
Completely inaccurate, at least for where I live. If it were true, the world would be a much less sad place. But reality cares not for cute kittens.

Here in the northeast US, feral cats (or even indoor cats with a comfy life) will never have two litters in a year. You are guaranteed one per year though. Maybe in Florida things are different.

Most kittens will never survive. We "had" one very feral cat. She would not even touch food we left out, until she was 20 years old and had cataracts in both eyes. Her secret to a long life? Dump all the kittens. Don't even let them nurse if you can help it. She had a dozen litters over the years. Most all died within two months, the lucky few lasted six. We buried all the ones we could find. Only one kitten of all her litters made it past a year.

The half life of a feral kitten is around three months. With a typical litter of five (including the runt who will get abandoned at a few weeks), maybe one will make it past a year. If no one starts feeding the extra cat, it won't even make it that long.

Edit: One final note. The life span and litter size of cats is very close to that of squirrels. True, squirrels have less environmental impact, being herbivores. (But this just means an environment could support an even larger number of squirrels.) The world is not drowning in squirrels (except for maybe Cornell) despite no one ever fixing the squirrels on their property.

I don't understand why it took over 3 hours to simulate 1000 iterations, I'm sure this could be done much more quickly, even with perl.

Wish the author would post source code.