I Which kind of function is this?

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The discussion revolves around identifying functions that could generate specific data patterns, with an emphasis on visual appeal. Participants express interest in complex functions, particularly 3-D fractals, while acknowledging that some proposed examples may not strictly qualify as functions due to multi-valued outputs. The conversation highlights the relationship between simple algorithms and the emergence of complex patterns, referencing Stephen Wolfram's work on the topic. The patterns discussed stem from mathematical operations like the modulus function, illustrating how simple calculations can yield intricate results. Overall, the exploration of function types and their visual representations reveals a fascination with mathematical beauty and complexity.
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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)

function.png


B)

function2.png


C)

function3.png
 
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I'd vote for some 3-D fractal, like this one maybe:
curling_up_by_batjorge-1024-768x768.jpg


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.
 
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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.

fmod-3.png

fmod-6.png
mod-8.png

mode2.png


mode.png
 
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Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

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