Is there some kind of standard equation for something that makes more of itself that makes more of itself etc. over a given period. For instance, say I built a robot over the course of 1 year whose sole purpose is to build another robot over the course of 1 year that does the same thing while I also built another of said robot. In 10 years with myself included how many robots would there be?

I'm not good at math, but I do like Excel. I believe you would have 767 robots at the end of 10 years. Can't help you with the formula equation...yet.

JoJo:
Sounds like you're looking for exponential growth:

https://mathbitsnotebook.com/Algebra2/Exponential/EXGrowthDecay.html

Interesting... I looked at that and googled it, I can't seem to figure out how to quantify the time value, such as 1 robot built per robot per year, or the results over the time period of 10 years on that equation. I also don't see any means of adding in a limiting factor, like say 1 robot can only make 4 robots before stopping.

I do not understand the maths, I've never really been able to, but I find myself wanting to figure out something like the example I posted, ergo this thread.

Bah, I was wrong. After ten years you would have 1,023 robots.

The expression is simple. It's 2^n-1.

The resulting answers should be: 1, 3, 7, 15, 31, 63, 127, 255, 511, 1023

Eh, I think they're called Mersenne prime numbers?

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The logic is very straightforward. After the first year you have one robot.
At the end of the second year you've made another robot, plus the robot you made prior also made a robot. That's three total after two years.

Year three you make another robot, and the 3 existing robots also make doubles, for a subtotal of 6. Plus your one that's 7 after three years. And so on.