Welcome to Fractal Forums

Hi, I looked around in this section and did a search but most, if not all, of the work being done with music using Fractal mathematics appears to involve the production of MIDI sequences and so forth. Great ! Love to see the experimentation and work  :dink:. But what I'm interested in is doing the audio/sound equivalent of what Mandelbulb 3D or Fractinit are doing. I have not seen any software yet that is doing what those applications are doing BUT ARE FOR SOUND. I think people make the mistake of trying to port a VISUAL fractal into sound. This is wrong. That kind of software is programmed from the bottom up to produce graphics for us TO LOOK AT. This is an entirely different set of problems and an entirely different domain to sound. Everything I've heard over the last 20 years that claims to be "Fractal music" sounds to, my ears at least, very little like what I am seeing in Mandelbulb 3D. I want to select a Fractal synth sound and have it sound as amazing as those Mandelbulb renders look !  O0 But the field of Fractals for sound and music seems to have been left behind, unless I'm missing something out there.

So are there any applications out there like Mandelbulb 3D, but for sound  ? I don't want applications that generate something visual and then transfer that to sound as that is fundamentally the wrong way to go about it.

I have tinkered with Pure Data ( https://en.wikipedia.org/wiki/Pure_Data ) before so plan to put my programming fingers where my mouth is if necessary, unless there's some huge software application that I've completely missed for some reason.

basically what you want doesnt exist.  its easy to say "fractals look cool, wouldnt it be neat if we could do that for sound."  but what would that actually be?  ... is basically a question nobody has come up with a good answer to yet, if ever they will.  short of like you say coming up with simple rules for generating sequences of notes.

Have you checked out Aexion's "Aural"?

http://www.auralfractals.net/

http://mathr.co.uk/blog/2016-04-15_nebulullaby_launch.html

I was also thinking a lot how to turn fractals into music.

Traditional music composes typically of a sequence of notes, which have pitch and rhythm. A still figure is then made of pixels with color. You can access each pixel whenever you want, and you dont have the concept of time there. There are not many similarities between a figure and music.
Color is something similar to timbre (sound color), but pitch or rhythm have no direct counterparts in figures.
I had to go to very basic fractals to find anything that could be turned into music relatively directly.
(If you havent heard my fractal music, it is here: http://www.fractalforums.com/fractal-music/two-fractal-music-compositions/ )

My fractals are quite far from the elegance of Mandelbrot, resembling more e.g. Koch snowflake.
However, at least some people seem to like how they sound.  The first visual fractals were quite simple, and only after some time more complex ones appeared. Perhaps more complex musical fractals with with more sophisticated structures are waiting for their finders.. :-)

Best,
Ville Pulkki

Did you see my thread on it? Haven't been much development since, but there are samples you can listen to....

http://www.fractalforums.com/new-theories-and-research/new-kind-of-'audio-fractal'-discovered

Thanks for your replies.

Been thinking about this. Of course much music is already a sonic equivalent of a Mandelbulber render. This is one of the reasons it sounds so good because it has inherent fractality in composition and at smaller and smaller levels. For example reverb and echo are inherently self similiar as evidenced by looking into a spectral waveform of the sound that when zooming in looks like finer and finer feather/wing like structures. I had a good example image of this and will post it here when I find it.

So just as Fractal software mimics the beauty of nature, music also reflects what we see around us in nature. As is pointed out in the article below music has always been algorithmic with composers using mathematical approaches well before computers. Apparently Mozart had a dice game he used to construct compositions.

Here is the article. A really good article about all this that goes into the entire history along with a few examples of actual applications.

Realtime Algorithmic Music Systems From
Fractals and Chaotic Functions:
Toward an Active Musical Instrument (http://mate.dm.uba.ar/~umolter/materias/geo-fractal-2-11/papers%20fractales%20y%20musica/fractal%20algorithmic%20music.pdf)

please do!! would love to see this visualized! :)

and while were at it:

good drumming is fractal: http://www.sciencemag.org/news/2015/06/secret-groovy-drumming-may-be-math
fractals in bachs music: http://mathtourist.blogspot.de/2008/09/fractal-in-bachs-cello-suite.html
fractal 1/f noise and other fractal occurences in music: https://courses.physics.illinois.edu/phys406/Lecture_Notes/P406POM_Lecture_Notes/P406POM_Lect15.pdf

and, my personal research: techno, especially psytrance/goa is a an acoustic cantor set. that one has been sitting on my to-do list a while, I need to write that article.. ;)
I also love that microphone or guitar feedback is the result of a recursive 'formula' and in my broad fractal view also is an acoustic fractal.

Is obvoiusly that a reverb is complicated and is ordered like a fractal. As example into chamber cube shaped if you clap you arms, the acoustical waves, will reflecting by walls, floor and ceiling but neperiodical becuase the sperical wave will knotting increasing harder becoming increasing dense. An example how clap sounding at minute {0; 1; sqrt(2); sqrt(3); 2; sqrt(5);...} but missing sqrt(7), sqrt(15), sqrt(23), sqrt(28), sqrt(31),... sqrt (4k*(7+8l)), but the intensity: 1;6;12;8;6;24;24;0;8;30;24;24;8;24;48;0;6;48;36;... at intervaly sqrt(n)

If you clap hands into cubed box at irrational distance of walls comparative with length , the sound intervals are like as this example:
17
53.7544467966324
72.2786404500042
88.7157287525381
109.033087246637
125.47017554917
143.994369202542
145.284271247462
161.721359549996
180.245553203368
180.748815999175
182.038718044094
198.475806346628
200.562911697466
233.437088302534
235.524193653372
237.317358494099
251.961281955906
270.191535099166
290.005630797458
290.508893593265
307.23992240591
308.52982445083
324.966912753363
326.76007759409
327.557280900008
345.787534043269
360.431457505076
362.224622345803
363.808464900834
364.311727696641
396.682641505901
397.185904301709
399.273009652547
415.71009795508
417.503262795807
418.793164840727
435.230253143261
436.027456449179
452.464544751713
453.251184000825
455.84155214747
473.568542494924
474.071805290731
490.802834103376
492.595998944103
505.152817055072
506.442719099992
506.945981895799
510.322989291556
523.677010708444
528.847182944928
541.907263851704
543.197165896624
543.491106406735
562.51856285591
563.51452439072
565.60162974156
578.15844785253
578.955651158448
598.769746856739
601.066174493273
614.912894649162
615.206835159273
618.28990204492
619.087105350838
633.940351098341
634.726990347454
636.814095698291
655.044348841552
668.39837025844
669.688272303359
670.485475609277
670.988738405085
671.481437144086
671.775377654197
672.781903245811
688.212465956731
689.218991548345
692.092736148296
707.743185201717
727.054018104201
727.263340389897
729.350445740735
741.404001055897
747.077436088189
759.928194709269
778.661710648337
779.951612693256
781.535455248287
782.541980839902
782.835921350013
784.125823394932
797.972543550821
798.979069142435
802.356076538193
816.496737204193
819.590368146645
820.880270191565
832.147186257614
834.234291608452
849.874176605068
851.667341445795
854.048387306744
854.25770959244
854.551650102551
855.547611637359
868.901633054247
871.984699939893
886.6286234017
886.922563911811
887.425826707619
891.306096899183
891.798795638185
908.235883940718
910.826252087363
911.120192597475
924.180273504251
925.764116059282
942.201204361815
943.700428692431
944.49763199835
946.08147455338
947.3713765983
947.874639394107
963.011261594915
976.86854580761
982.332658554205
995.392739460982
999.765708391548

This is generated with VISUAL BASIC with the code:
Sub test2()
Dim a, b, c, et, nn, nm As Long
Dim na, nb, nc, rez As Double
Dim coada1(1 To 1000000) As Double
Dim coada2(1 To 1000000) As Double
et = 1
For a = 1 To 100
For b = 1 To 100
For c = 1 To 100
na = (Sqr(2) + (a - 50) * 10)
nb = (Sqr(5) + (b - 50) * 10)
nc = (Sqr(10) + (c - 50) * 10)
rez = na * na + nb * nb + nc * nc
If ((rez) < 10000) Then
                   Debug.Print (rez);
                   Debug.Print (" ; ");
                   coada1(et) = rez
                   et = et + 1
                   End If
'Debug.Print (rez);
'Debug.Print (" ; ");
Next c
Next b
Next a
Debug.Print ("=")
For nn = 1 To et
'Debug.Print (coada1(nn))
For nm = 1 To nn
If (coada1(nn) < coada1(nm)) Then
                              coada2(nm) = coada1(nn)
                              coada2(nn) = coada1(nm)
                              coada1(nn) = coada2(nn)
                              coada1(nm) = coada2(nm)
                             End If
Next nm
'Debug.Print (coada1(nn))
Next nn
For nn = 1 To et
Debug.Print (coada1(nn));
Debug.Print (" : ");
Next nn
Debug.Print ("=")
End Sub

Yep. Most things have some kind fractal dimension including music and reverb, echoes. But its not quite the idealised, designed fractals that can be created in eg. Mandelbulber 3D. That's an intentional fractal approach from the start whereas a lot of music is accidentally - if naturally - created fractals.


See attachement. That's from a drum machine/303 Rebirth track that I did. That part to me at least looks fractally. Somewhat like bird feathers.


Yes, I was just looking at the Cantor set related to yin/yang & Hexagrams.


A lot of music is very mathematical. I suppose a mathematician would say everything can be explained mathematically. I've found guides/scientific papers using modular synths to recreate formula’s using the various modules of the synth.

The basic thing is this: an image of a fractal is a single frame. A single "slice" of time. Rendered pcm audio to make a "synth" sound, maybe in real time (but complex fractals I guess ain't gonna happen in realtime) has a time domain to it. I'm thinking of something like SimSynth 1.0 from way back in 1994 where you could define the sine waves and so forth using numbers that were entered and it would render a sound (EDIT: actually I think I was thinking of an old version of Cool Edit, think the same thing can be done in Audacity). I think PureData and other software can do this.

So. A fractal SOUND is happening in a time domain. This sounds a bit like rendering an animation of a fractal in Mandelbulber or whatever application. So a fractal synth sound would not be akin to a single fractal image but with THE CHANGES that happen over time that we can see in fractal animations. Of course that all has to be translated in some rational way to the pcm data; frequencies, amplitude, envelope, stereo (surround sound ? but most people just have 2 speakers). I'm thinking of the basic raw material of a sound effect before sequencing, arpeggiation, etc.

I wish topics wouldn't fall out of sight so fast here.
I missed your answer completely, djbarney!
fascinating, I totally agree, especially the "single slice of time" part..  thx for sharing your thoughts!

Cheers. A lot of the problem seems to be the conceptualisation in order to actually start writing algorithms in SuperCollider or whatever. I got diverted by other matters but am subconsciously thinking about this. Although I did get into a twitter exchange with BT about this - https://twitter.com/BC_Man/status/732673365467660288 ... still puzzling over why he needs to make fractal sounds "by hand" ?