I'll answer your questions in order:
1. I find the result of growing inequality out of randomness puzzling. Is there an intuitive explanation for this outcome?
My response required some math, so I've attached a pdf.
The short answer is no ... I think this stuff is unintuitive. But the mathematics is straightforward.
2. How is the model bounded?
The only bound is the distribution of growth rates. Growth rates come from an exogenous distribution, determined by me. The total market value of all investors will vary dynamically, depending on the parameters of the growth rate distribution.
3. Have you run this simulation using different parameters/assumptions?
Yes. I've made more videos.
Here is a model where market gains have a mean of 0 and a standard deviation of 1%: https://www.youtube.com/watch?v=u9HO-eBVVII
Inequality grows very slowly. The standard deviation controls differential growth
which is what ultimately causes inequality.
Here is a model where market gains have a mean of 1% and a standard deviation of 2%: https://www.youtube.com/watch?v=FJtTD4p62A8
Average net worth increases with time (as we might expect), but inequality also grows. The distribution propagates through "space".
Here is a model where market gains have a mean of 3% and a standard deviation of 8.5%: https://www.youtube.com/watch?v=0OnDcpzk1Zo
Both average net worth and inequality increase rapidly.
So to summarize, the growth rate mean determines how quickly (if at all) the distribution will move through "space", while the growth rate standard deviation determines the rate of increase of income inequality.