Brownian Motion

Questions and Answers
1

I was wondering how I might implement brownian motion with Tidal. I was thinking you could use state to add a random value (with a specified range) to an existing variable. Unfortunately I don't know enough about haskell to go about implementing this

The use case is a control pattern like # pan "variable" where the variable is updating every cycle with a new number that's randomly incremented.

2

use markovPat (for a fixed, finite set of pan values). Something like

d1 $ s "casio:1"
   + pan (let n = 8
          in fmap (\ i -> fromIntegral i / n)
            $ markovPat n 0
             [[  if abs(x-y)== 1 then 1 else 0 | x <- [0..n-1]]| y <-[0..n-1]]
              )

incidentally, why does the source have

{- @markovPat n xi tp@ generates a one-cycle pattern of @n@ steps in a Markov ...
^^^^

this should be {-| (for haddock)?

3

I made another realization of randomly increasing sequences, using the scanl function (
Data.List ) . For a sequence xs, the sequence scanl (+) 0 xs contains the partial sums, e.g.,

ghci> scanl (+) 0 [1,0,1,0,2,0,1]
[0,1,1,2,2,4,4,5]

in the following code, the elements of the list are patterns, not plain numbers - I only use that to get some randomness. From that, scanl (+) 0 makes a randomly increasing sequence, and I play that, in parallel to its mirror image (decreasing). And I drown it in reverb. Have fun.

(code: tidal/code/scanl.tidal · master · waldmann / computer-mu · GitLab , audio: tidal/code/scanl.ogg · master · waldmann / computer-mu · GitLab )

1 Like
4

I don't know how this solution compares to other options, but there's already a sort of state implemented in Tidal: State Values | Tidal Cycles

Normally the way those states are updated is to always rise by 1 modulo some divisor. That has the strange effect that reversing the rising sequence results in another rising sequence, not a falling one. But anyway, if you hacked into that and replaced the function that increments things with a function that adds a random value, you'd have Brownian motion.

There's the nuance that random sequences in Tidal require IO. If you're a fan of purity -- which you should be :wink: -- you can restrict that IO to the top calling levels by writing deterministic functions that receive a random sequence from on high.