I'm trying to figure out how a new civilization would grow on a world with only a ship of 200 people that dropped accidentally out of hyperspace. They set up a city based on the Law of Ara and their Scripture. Then develop a school for training people to venture out and establish new cities. During this colonization process, one of the leaders declares himself a prophet with new additions to their book of scriptures. Some join him and then he has "prophecies" which say those who claim to be Arakun who do not follow him must be captured and killed if they refuse to follow God's Prophet.

Many battles ensue, even a few world wars. This was meant to be the background to a civilization where one man has developed DNA robots and plans to use them for eugenic purposes.

I'm not sure how many hundreds of years would have to pass before getting to that point technologically. I'm trying to incorporate slow growth technologically when wars are being fought, and then maybe even as they try to rebuild in the aftermath, leading up to some periods of prosperity where they could focus on science.

I assume they would have some technology on their ship, but what do they use for power? I'm going to go with solar power and maybe even nanotechnology. If they already have this basis, how long would it take to replicate on a planet without any manufacturing plants to produce the materials needed to build what they need to execute their technology?

I assume they would have solar power and nanotech because any civilization capable of hyperspace travel likely surpassed their nonrenewable fuel stage. That being said, they would likely not begin this new world using nonrenewable fuels. So, how long before DNA robots? This may be a dumb question, because it seems likely that we may develop DNA robots around the same time nanotech and solar power become major influences in our society. I suppose DNA robots might not have been developed yet in their original world. Maybe they don't even really understand the tech they used to get to this new world, and then it would take a while for someone to learn how to utilize nanotech through reverse engineering.

I'm shooting for between 500-900 years.

As I write this though, it makes me wonder if it makes sense for my hero to be someone who developed a local crop into a fuel capable of fueling flying personal transports. Unless, this happens far closer to when they arrive and the bad guy who comes up with DNA robots is a descendant of one of the original members who taught his research down by generation until it reached him. Oh, I think I like this...

With a nation of two hundred people, if there were one hundred family units, each with two kids, that would increase the number to four hundred. After one generation. I won't calculate it all out, but maybe you could look at the time it takes for a 'world' to grow out of two hundred people and use that as your time frame?

The more the population increases the faster the rate of growth increases. Naturally, as more people are in the world, there will be more people studying the sciences and stuff. But if that takes too long, perhaps you could have a competition between rival scientists to develop the DNA robots.

And if they have solar and nano technology, it's safe to say that they could develop DNA robots, however, they are completely alone, so even if that would have been easy on another planet with a huge group of scientists, they have only a few...so naturally it takes them a few hundred years.

Thus, you could have a timeline like this:

0: Ship arrives with solar and nano tech.
100: As colony expands (maybe four generations later) the guy comes as a prophet and splits them.
100-500: Series of wars and population growth slows because of the wars. But at this point you've still only got a population of thousands, I think.
600: Both rival sides develop, within a few years of each other, DNA robots

Wait a minute, you just totally changed the plot at the end there. So they've had DNA robots for a long time? Or they've been a secret of one family? I didn't get your change of plot at the end.

Sorry about the confusion at the end. I had this idea that my antagonists great great....grandfather had the initial research but it was not complete. Vil could complete the research, either by finding long lost documents/files or by applying needed catalysts like a biowar to funding the research. I'll think about this more.

Thanks for your thoughts on pop growth. More to think about. Maybe the ship was larger...

Depending on the technology of the original ship they came in, it's probably not unlikely that it could hold a few thousand people...that would speed up pop growth.

eruheran

Within 600 years, factoring in the wars, there would be between 40,000-60,000 people, with 200 people on the orginal ship. If you put one-thousand people on the ship, there would be from 200,000-300,000 and double that if there were 2,000 on the ship.
Hope my number punching helped, if you hadn't figured it out yet.