Mathematician Application

Hi,

My name is Jon and I am a PhD student in mathematics. I study Dynamical Systems and more specifically PDE's. I'm really interested in the deployment of differential equations in games (I love games  :D and was really hopeful for spore but  :evil: ). I think the game design questions are fascinating.

For example I had a look at this page

https://thrivegame.canadaboard.net/t933-population-dynamics

and I like what you are talking about and it throws up a whole load of interesting questions.

So when you have several species and their equations are coupled together what kind of dynamics do you want?

For example if you do nothing but leave the game alone for a long time without making any changes to the environment should the different populations all converge to stable equilibria? Should there be a limit cycle where by the populations are all fluctuating together? Should there be a chaotic attractor (which is where a lot of my work is) so there are non-predictable fluctuations (it'd be a really interesting feature if every time you loaded a save and made one change the game flew off on an exponentially diverging trajectory)? Or do you want something unbounded?

Should a predator be able to eat their prey to extinction and then die themselves or do you want a lower bound for population? How you design this is quite important as it's lame if you just say that the minimum population of grass is 10 because then you could have a player who tries to eat it all and just gets stuck against an invisible wall.

However if you say the breeding rate for grass is proportional to it's population so it blows up at zero then you get a really cool system where you try and eat the last of the grass but it just breeds faster and faster the less of it there is so you can never quite make it. Much more interesting and smooth.

Though you may want the predator to be able to eat all the grass.

There are loads of cool things to consider like this as the game lies somewhere on a spectrum from simulation to play experience and you want to make it "feel good". Unpicking what that means is fascinating.

Also I don't know how you're planning to deal with spatial distribution (for example of grass on a planet) but there PDE's come into play and things get cranked up a notch.

Anyway I can't offer a lot of programming however I am more than happy to discuss any mathematical elements of the game and would enjoy to do so. Differential equations are going to run through the whole course of the game so it's going to be a really good source of problems for me.

Let me know if you are interested.

Good to have another hand on deck

Math, being both the language of code and science, is immensely helpful to the project (especially with so much experience). As you mentioned, one application of that in the project is in population dynamics, but for specific questions on that you'll be better off with moopli, crovea, or seregon, who know more on the subject.

I know the coders are also working on a dynamic membrane generating system, and given your lack of coding experience I don't know how much you could help them there but here's a cool video showcasing an early prototype:

https://www.youtube.com/watch?v=W20rDBK70_0

Also, we opened a new subforum recently called Technical Discussion. Feel free to use it to post threads on interesting prototypes, procedurals, studies, or other cool content you may find that could contribute to development in some way.

Other than that welcome to the team!

Hi Jon, and welcome to the forums.

It sounds like you've got some interesting suggestions, and the knowledge to back them up. I've always wanted to have a deeper discussion about some of the ideas in the population dynamics (and similair) threads, so if you want to restart any of them, please do.

I haven't been very active on the forums for several months now, as I've had plenty of interesting problems to think about at work, restarting some of the technical discussions might be just what I need to tempt me back though.

I'll take the rest of your questions as examples, rather than responding to each of them (if you want a specific answer to one do say so though!), except to say that while we didn't get as far as discussing specific dynamics, thats definately something we need to do if we want to implement population dynamics fully, and its something i'd be keen to go into at some point.

Any other questions, feel free to ask them here, or in the relevant thread (necroposting is fine, but only if your adding to, or starting a constructive discussion, not for unnecessary comments or suggestions).