Looking for math/physics modelling software

I’m on a Mac, and looking for math/physics modelling and/or graphing software recommendations. Free is of course best, but would look into non free software that can do what I want. Here’s some examples of the sorts of things I’d like to do:

  1. Game of Life type simulations, playing around with different permutations of neighbor rules. Or slightly more complicated AI type things with basic behaviors.

  2. 2D gravitational attraction simulator - i.e. determine placement of object and their mass, and see how they move based on those variables. More importantly, I’ve always wanted to play around with the same scenario, but on the surface of a sphere.

  3. I’ve often wondered what the path of those series of concentric rings would look like it plotted (think the machine from Contact).

  4. Plot an equation, and then convert the resultant graph into an audio file.

I think you get the idea. Would something like Mathematica or Processing do the trick? Some other software? Or would it be easier or necessary to just learn some kind of programming language (the easier to learn the better). I’ll note that I did manage to program something similar to the first part of #2 in MAX many years ago, which wasn’t terribly difficult since it was object based. Any ideas?

I think Mathematica would work well for many of these things. I don’t know if it is available for the Mac but would bet so.

You might consider FlexPDE for some kinds of things. It is available for the Mac. It gives solutions to partial differential equations in field variables, which is a category of computing that has an amazingly broad range of application. It is truly a fine program and you can evaluate demo software if you like - they have a student version, too, that is inexpensive.

There is indeed a Mathematica for the Mac and it sounds right up your alley for the equation modeling.

For cellular automata and other agent-based modeling, if you don’t mind doing a bit of very simple programming (really more like pseudocode) then I recommend NetLogo, which is free!

Mathematica does cellular automata like the Game of Life - cellular automata are Wolfram’s “thing”. It’ll do the rest as well, though MATLAB may be better for huge numerical systems.

Both are available for Mac; neither is what you’d call “cheap”.

I have essentially no knowledge about this type of software (and don’t really even understand what you want to do with it) but if you’re interested in free, there is an open-source version of Matlab called Octave (or qtOctave if you want a GUI and not a command line). I use the latter for very simple problems in a Numerical Analysis course, but I’m told it’s much more powerful than what I’m doing!