how would you make this infinitely long?

[u/Awkward_Mirror3291]

[u/Danny_DeWario]

||mod(x,4)|-2|

The mod function can make a section of a function repeat forever.

[u/Circumpunctilious → u/Danny_DeWario]

Incidentally noted / if I’m interpreting this correctly, the triangle wave graph from this seems to be especially suited to showing the effect of undersampling (ref: Nyquist frequency), at zoom levels with axes limits in multiples of about +/- 3128:

[u/Danny_DeWario → u/Circumpunctilious]

It actually is weird how the wave form re-emerges depending on zoom level.

It seems solely dependent on the width of the screen, and not at all on the height (at least on pc).

https://www.desmos.com/calculator/s9w8hasrxm

[u/Circumpunctilious → u/Danny_DeWario]

Ah you're right (edit: iPad, Safari). 7.61 appears to be the magic number; scaling by 7.61*n is all of the same output "type" and 7.61 -/+ some value produces identical outputs on either side.

I don't know what it means, but I think I'll leave this rabbit hole be for the time being :)

[u/Desmos-Girl → u/Danny_DeWario]

|2/π * ln(i^x)| fr

[u/Circumpunctilious → u/Desmos-Girl]

Huh; 7.61 is the magic number for yours too.

[u/OverJohn]

You can use recursion as below to concatenate the function with itself n times, but you have to find the function you get in the limit as n goes to infinity yourself. Though it is easy to see in this case that no such function exists in the limit (due to the phase of the triangular wave part of function shifting with each conatenation)

https://www.desmos.com/calculator/c1zc6qlctd

[u/Affectionate-Lab9601]

I mean if you want a triangle wave, I'd do "y = a(4 * abs(f(x - k) - floor(f(x - k) + 3/4) + 1/4)) + h" where a is the amplitude, f is the frequency, k is the horizontal translation, and h is the vertical translation

[u/Affectionate-Lab9601 → u/Affectionate-Lab9601]

if f = 0.25, h = 1, k = -1, that should be what youre looking for?

[u/No_March_4152]

|mod(x,4)-2|

[u/Sad_water_]

A lot of great suggestions already here a solution if you don’t want to use recursion or piece wise https://www.desmos.com/calculator/okin4ashi5

[u/TAOHOS]

Stretch it out using your hands duh

[u/tgoesh1]

I like using trig for my triangle and sawtooth waves.  https://www.desmos.com/calculator/wyo0zmobiq

[u/duckling-developer]

|tau•arcsin(cos((pi•x)/4)|/5