> Rolling one die at a time, or two,

Read: Rolling one die at a time, OF two,

> On Jun 27, 2019, at 9:00 AM, Nigel Redmon <earle...@earlevel.com> wrote:
> 
> 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 
>> <mailto: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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