^Kyriakos is right. That has already been attempted, by community members who (as I understand it) had as many resources and connections as can be expected here.
WildWeazel, I think your suggested approach is along the right tracks. Minimally playable game and hotseat are two particular ones that I think are wise, limited initial goals. Trying to do everything up front would be way too much; simply displaying sufficient graphics to have a game is itself a significant hurdle. I'd probably leave off square/hex/isometric and just go with one - isometric if you want to be able to re-use existing graphics - since I suspect supporting more than one would drastically increase the complexity of the code needed to handle game rules (unit attack, movement, route calculation, connected cities, multiple types of graphics, etc.).
The age-old debate is open-source versus closed-source, and free versus commercial (there have been free, closed-source attempts). I also think free, open-source is the best approach. Could someone try to do the commercial route? Yes... but what are the chances of success? You might as well try your own original idea without the restrictions of being similar, and that's not even counting the potential hazards of trying to commercialize something that is intentionally similar to an old game. Dedicating enough time to a game to get it off the ground within a reasonable period of time would also require more time than most people with a day job have, which pretty much limits it to those who are retired or financially self-sufficient... and if that describes you, and you want to make a Civ3 clone, why would you bother commercializing it?
Not that making it open source will necessarily speed up development by having multiple contributors. But it does allow the possibility, which previous attempts have not. And even if the attempt fizzles out, someone can pick it up again later. The local Civ1 clone has had
contributions from five people other than the initial creator, and while the initial creator is still responsible for 99%+ of the code, it's something.
What we do need is a leader with time to dedicate to getting it off the ground, and enough expertise to build enough that people start seeing it as a real project that could go somewhere. Finding someone with both of those has proved challenging. Those who have attempted have not had enough time to get quite far enough before life circumstances reduced their available time. And I know that realistically, I wouldn't have the time even if I had the skills.
But if that leader can be found, I'd be interested in contributing occasionally. The one area I wouldn't be of much use is the graphics, as I essentially know nothing about that (which I know sounds odd since I'm the person who wrote an editor with a visual map component, but that was learning as I went, slow going, and would probably horrify someone who knew what they were doing in the graphics department). But general program logic, reading in data from various formats, even networking and perhaps some sort of AI I could contribute to, and if something got off the ground I could probably be convinced to dust off some rusty knowledge of whatever programming language was chosen.
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On a different note, has anyone else thought about implementing Civ3 within the Civ4 engine? Other than the obvious isometric vs squares difference and the subsequent effect on graphics, and the fact that scenarios wouldn't be automatically playable, I suspect you could re-implement the rules as Civ3 has them. The interface is at least somewhat customizeable to new concepts (Nathiri's post reminded me of this), and the AI is scriptable as well, so you could teach it to use any concepts that Civ4 doesn't have, and probably wind up with a better AI than Civ3 eventually. You could also keep any parts of Civ4 you liked, such as religion. It would still be a massive undertaking, which is why I haven't tried it, but probably less so than starting from scratch. And it would allow us to get around several of the common Civ3 limitations, such as 31 civs, though admittedly perhaps trading them for others, such as higher memory usage. Other Civ versions as a base might also be possible, but AFAIK Civ4 is the pinnacle of Civ customizeability, which would seem to make it the one to choose.