brownian bridge

[AM]

i like the concept of "brownian bridge" to produce complex curves from a to b, but not completely randomized or controlled. in the video you see all the generations for one evaluation...

 

how it could sound - mapped on different tonalities

 

 

 

Brownsche Brücke – Wikipedia

DE.WIKIPEDIA.ORG

 

for understanding in OPMO:

 

axiom: start end

(50 23)

 

gen1 => 1 step

(50 8 23)

 

gen2  => 3 steps

(50 15 8 -3 23)

 

gen3 => 7 steps

(50 40 15 13 8 -14 -3 29 23)

 

gen4 => 15 steps

(50 58 40 33 15 22 13 4 8 4 -14 -16 -3 17 29 17 23)

 

...and so on

 

-------------------------------------------------------------------------------

 

some evaluations with same AXIOM:

 

 

 

;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
;;; BROWNIAN BRIDGE -> could be use as a rnd-process from A to B (integers or pitches)
;;; if you have a look to example with ":all-gen t", you will see the process with all generations, how it works

;;; or take a look to:
;;; https://de.wikipedia.org/wiki/Wiener-Prozess#/media/File:BrownscheBewegung.png
;;; https://de.wikipedia.org/wiki/Brownsche_Brücke
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;;; SUB

(defun pick (a b &key (span 5))
  (let ((rnd1 (car (rnd-number 1 (+ a span) (- a span))))
        (rnd2  (car (rnd-number 1 (+ b span) (- b span))))
        (n))
    (progn
      (setf n (car (rnd-number 1 rnd1 rnd2)))     
      (if (or (= n a) (= n b))
        (+ (rnd-pick '(1 -1)) n)
        n))))


(pick 2 3)


;;; MAIN

;;; MAIN

(defun gen-brownian-bridge (n startend &key (all-gen nil) (output 'integer) (span 5))
  (let ((seq))
    (progn
      (setf seq (append (list startend)
                        (loop repeat n
                          with liste = startend
                          do (setf liste (filter-repeat 1 (loop repeat (1- (length liste))
                                                            for cnt = 0 then (incf cnt)
                                                            append (append (list (nth cnt liste) 
                                                                                 (pick (nth cnt liste) 
                                                                                       (nth (1+ cnt) liste) 
                                                                                       :span span)
                                                                                 (nth (1+ cnt) liste))))))
                          collect liste)))

      (setf seq (if (equal all-gen t)
                  seq
                  (car (last seq))))
      (if (equal output 'pitch)
        (integer-to-pitch seq)
        seq))))
  

;;; EXAMPLES


;; SPAN influence -> span 2
(loop repeat 20
      do (list-plot (gen-brownian-bridge 5 '(1.2 5.4) :span 2 :all-gen t)
                    :zero-based t
                    :point-radius 3
                    :join-points t)
         
        do (sleep 2))  
         

;; SPAN influence -> span 10
(list-plot (gen-brownian-bridge 5 '(50 23) :span 20 :all-gen t)
           :zero-based t
           :point-radius 3
           :join-points t)

;;; SPAN default (5)
(list-plot (gen-brownian-bridge 5 '(50 23) :all-gen t)
           :zero-based t
           :point-radius 3
           :join-points t)

(list-plot (gen-brownian-bridge 5 '(50 23))
           :zero-based t
           :point-radius 3
           :join-points t)


(gen-brownian-bridge 5 '(50 23) :all-gen t :output 'pitch)
(gen-brownian-bridge 5 '(50 23) :output 'pitch)

 

[opmo]

(defun gen-brownian-bridge (n startend &key (all-gen nil) (output 'integer) (span 5))
  (let ((seq)
        (liste startend))
    (progn
      (setf seq (append (list startend)
                        (loop repeat n
                              do (setf liste (filter-repeat 1 (loop repeat (1- (length liste))
                                                                    for cnt = 0 then (incf cnt)
                                                                    append (append (list (nth cnt liste) 
                                                                                         (pick (nth cnt liste) 
                                                                                               (nth (1+ cnt) liste) 
                                                                                               :span span)
                                                                                         (nth (1+ cnt) liste))))))
                              collect liste)))
      (setf seq (if (equal all-gen t)
                    seq
                  (car (last seq))))
      (if (equal output 'pitch)
          (integer-to-pitch seq)
        seq))))

 

Small change otherwise you get:

Warning: Local Variable Initialization clause (the binding of liste) follows iteration clause(s) but will only be evaluated once.