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Awesome Article! Something This relates to is data compression. The way I've always imagined time travel was as if the world was x,y,z,t. This is easily done when all calculations are mathematically handleable as its an f(t) equation, however creating those equations is far less easy. When a random seed exists it can still be done though it would be computationally expensive since each time a random is retrieved is an important difference from other worlds. The saving the player data as you put it seems extremely difficult as you would have to save every single choice and the tick it happened. This is similar to what you mentioned only saving variables as they changed but you probably saved each npc's data as well (which would make regeneration much faster). This relates to data compression because it is unknown what the next byte will be, only that there are a series of them. Additionally, writing a streaming compressor that easily streams back out again isn't as easy as I want to believe it is.
Thanks! I had the impression that it could be thought of data compression. I'm more skeptical of your f(t) idea. Sure, it could be thought of that. But could you calculate that function in any less time than it would take you to run the simulation? I would guess not, but I'm not sure.
You have every right to be skeptical and, to be honest, I prefer to be naive when coming up with these types of hypothesis so that I dont lose hope too easily.

With physics this is somewhat easier to do as I am able to calculate position in time, gravity and collisions (so long as they are easily solvable. I actually tried to rebuild a verlet physics engine to do this with, some success but ultimately failure.

For a game such as yours there is no floating point physics. It seems to be based off AI mostly which involves far less equations and far more 'what the hell is going on and what do I do'. As a result, you probably dont have the liberty thT I did.

I actually am interested in your game because its ambitious and yet you have the hunger and cleverness to pull it off.