I think this becomes more obvious if you separate out the random and the 
filtering:

Rolling one die at a time, or two, is equivalent to rolling one die, but 
writing down or remembering the previous value before the roll. In there words, 
it’s like a like having a delay element to use for the sum or difference, and 
that gives the lowpass or highpass response.

But if we remove the filter and just look at rolling dice:

Rectangular PDF: roll one die each time

Triangular PDF: roll two dice each time, take the sum

Gaussian: roll a bunch of dice (to whatever degree of accuracy you want, but 
six is pretty good) each time, take the sum

So, if you want the same highpass filtering as the algorithm you gave, but with 
Gaussian noise, generate Gaussian, then run it though a one-zero highpass.

As to whether that’s worth it…I assume you’re just experimenting


> On Jun 27, 2019, at 7:42 AM, Alan Wolfe <alan.wo...@gmail.com> wrote:
> 
> I read a pretty cool article the other day:
> https://www.digido.com/ufaqs/dither-noise-probability-density-explained/ 
> <https://www.digido.com/ufaqs/dither-noise-probability-density-explained/>
> 
> It says that if you have two dice (A and B) that you can roll both dice and 
> then...
> 1) Re-roll die A and sum A and B
> 2) Re-roll die B and sum A and B
> 3) Re-roll die A and sum A and B
> 4) repeat to get a low pass filtered triangular noise distribution.
> 
> It says that you can modify it for high pass filtered triangle noise by 
> rolling both dice and then...
> 1) Re-roll die A and take A - B
> 2) Re-roll die B and take B - A
> 3) Re-roll die A and take A - B
> 4) repeat to get a high pass filtered triangular noise distribution.
> 
> What i'm wondering is, what is the right thing to do if you want to do this 
> with more than 2 dice? (going higher order)
> 
> For low pass filtered noise with 3+ more dice (which would be more gaussian 
> distributed than triangle), would you only re-roll one die each time, or 
> would you reroll all BUT one die each time.
> 
> I have the same question about the high pass filtered noise with 3+ more 
> dice, but in that case I think i know what to do about the subtraction 
> order...  I think the right thing to do if you have N dice is to sum them all 
> up, but after each "roll" you flip the sign of every die.
> 
> What do you guys think?

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