Which kind of function is this?

[Jarvis323]

I'm curious how close someone could get to guessing the functions that generated the data shown below. And also, without looking at the plot, what do you think would be the most interesting looking function of x,y,z you can think of.

A)

B)

C)

 

[DaveE]

I'd vote for some 3-D fractal, like this one maybe:

edit: I guess this isn't a function though. More like an algorithm. Functions can't be multi-valued, right? Plus maybe you mean 4-D; "a function of x,y,z". Anyway, I like the pictures.

 

[sysprog]

The patterns could be viewed as complex emergent phenomenomena produced by combinations of simple algorithms, with various input parameter sets., e.g. as in Stephen Wolfram's A new Kind of Science [Substitutions and Fractals (in Chapter 5)]

 

[Jarvis323]

They're each some functions that combine sinusoidal and the mod function.

It's pretty interesting to me the patterns the come from just taking the remainder.

Each of these are just fmod( i*j*k, r ) for different r.