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
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

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