Structure from Chaos: Fractals Generated on the Circle of Fifths via the Chaos Game

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Running the chaos game on the circle of fifths, producing music to accompany the beautiful fractals that result.
We start using a triangle on the notes C, E, and A♭ (forming an augmented chord), and play the chaos game to generate the Sierpiński triangle.
Then we use a hexagon on the notes C, D, E, G♭, A♭, and B♭ (a whole-tone scale). For optimal packing, the ratio used to divide the lines in the chaos game is 0.667 for a hexagon.
Next we use all 12 notes (the chromatic scale) to form a dodecagon fractal. The dodecagon is optimally packed with a ratio of 0.789 to divide the lines.
Finally, we use a square (i.e. a diamond) on the notes C, E♭, G♭, and A (forming a diminished 7th chord). Playing the normal chaos game on a square, however, doesn't yield a fractal. It only produces uniform noise within the square. When a simple restriction is added: not allowing any corner to be repeated twice in a row, a beautiful fractal results.
0:00 Sierpiński Triangle
3:54 Hexagon Chaos Game
7:05 Dodecagon Chaos Game
10:27 Square Chaos Game
________
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#fractal #math #music #beauty #art #mathematics #code #programming #computerscience #processing #java #visualization #algorithmicmusic #computermusic #experimental #hypnotic #randomness

Пікірлер: 96

  • @Vindilax
    @Vindilax2 ай бұрын

    4:52 its amazing how similar this sounds to Chamber of Sages from Legend of Zelda.

  • @grishhung2828

    @grishhung2828

    Ай бұрын

    It's the whole tone scale! That specific series of six notes, do, re, mi, fi, si, and li (which are, in this case, C, D, E, F#, G#, and A#) are often used for making mysterious, dreamlike songs in movies and video games. Each note is spaced two semitones apart. It sounds particularly like the Chamber of Sages here (which also uses this note set) because we're in the same key (C).

  • @TylrVncnt

    @TylrVncnt

    Ай бұрын

    Haha thought the same thing g

  • @baefaux

    @baefaux

    Ай бұрын

    It even looks a bit like the chamber of sages from top down too

  • @dragonfire.8271
    @dragonfire.8271Ай бұрын

    So um, for the square: Yes it will not work if the line ratio is 0.5. Cuz in order to the sierpinski carpet to be made, you need the line ratio to be 2/3 at a random vertex AND MIDPOINT. So restricting the process is the only best way if you run the chaos game to the circle of fifths

  • @CiscoWes
    @CiscoWesАй бұрын

    Played the video too loud and my furniture started to levitate. And I think I opened a portal.

  • @channalbert
    @channalbert2 ай бұрын

    9:00: Coltrane is jealous.

  • @BA-we6bv
    @BA-we6bvАй бұрын

    Me trying to do every combination lock to get in my brothers phone:

  • @BlackMoonMaster
    @BlackMoonMaster2 ай бұрын

    i love fractals

  • @Nivaleia541
    @Nivaleia541Ай бұрын

    Why is 0.789 used on the dodecahedron fractal?

  • @MrEthanhines
    @MrEthanhines2 ай бұрын

    Must be what Spielberg was thinking b4 he made close encounters

  • @blobby-ur7vn
    @blobby-ur7vnАй бұрын

    it would be interesting to hear what a different selection of notes assigned for the octaves or halving of the distances between the two points instead of repeating the same pitch. eg run through the harmonic series using that note that is being halved as the fundamental, eg at 0.49 E, E, B, E, G#B, D and based over a C fundamental C, C, G, C, E, G, Bb and etc

  • @marceloislas1413
    @marceloislas1413Ай бұрын

    That is more the result of the chosen method rather than something to do with notes and music.

  • @watchtowerdragon7098
    @watchtowerdragon7098Ай бұрын

    Chaos Within Structure = Structure Within Chaos

  • @twbvqc
    @twbvqcАй бұрын

    i just listened to fractals for so long

  • @stanley9252
    @stanley9252Ай бұрын

    Nice video! I had no idea about "chaos games". I'm curious, though, what language and libraries are you using for visualizing these fractals and playing the notes?

  • @OLIVE_MANN
    @OLIVE_MANN21 күн бұрын

    When are you releasing on spotify

  • @reid_makes_art
    @reid_makes_art2 ай бұрын

    Super cool channel man!

  • @jacpa2011
    @jacpa20112 ай бұрын

    Its nice you doing other sort of content!

  • @sistajoseph
    @sistajoseph2 ай бұрын

    Beautiful

  • @holyelephantmg8838
    @holyelephantmg883824 күн бұрын

    2:25 *insert Zelda chest opening theme here*

  • @Poetateoe
    @Poetateoe23 күн бұрын

    Why was 0.789 used for the Dodecahedron? Curious to look further into it

  • @morgunstyles7253
    @morgunstyles7253Ай бұрын

    Great video

  • @D4N15H_
    @D4N15H_Ай бұрын

    1:35 The sound is like c418 - cat

  • @TZG-cr1uc
    @TZG-cr1uc2 ай бұрын

    The sounds are satisfying

  • @maxdoubt5219
    @maxdoubt521912 күн бұрын

    So cool! Like a treasure hunt.

  • @EntergeticalakaBot
    @EntergeticalakaBot2 ай бұрын

    Algomotion voice jumpscare???

  • @DaveLopez575
    @DaveLopez575Ай бұрын

    3:25 fractal sounds.. awesome 😎

  • @jaydensanimations7022
    @jaydensanimations7022Ай бұрын

    7:01 Now *that* is what I call, the Koch Hexagram!

  • @juanpabloaraujotome5272
    @juanpabloaraujotome5272Ай бұрын

    Sumamente interesante, saludos desde uruguay

  • @LukesTheBomb
    @LukesTheBomb17 күн бұрын

    THE TRIFORCE IS REAL!

  • @lyanporto
    @lyanportoКүн бұрын

    on the first one if you started with a point that doesn't lie on the triangle, or if the first line's middle point doesn't fall in the triangle, would it still work?

  • @jonatandjurachkovitch460
    @jonatandjurachkovitch46029 күн бұрын

    But this is true for any triangle, why the circle of fifths?

  • @davidknopp1208
    @davidknopp1208Ай бұрын

    It’s the trifor

  • @HalfBreadOrder

    @HalfBreadOrder

    Ай бұрын

    y

  • @alexaleman16
    @alexaleman16Ай бұрын

    Sounds like hitting the jackpot on a slot machine, or so ive heard 😂

  • @deathhzrd
    @deathhzrdАй бұрын

    The dodecagon is super cool

  • @juanpalml7
    @juanpalml78 күн бұрын

    What if you select a dot inside of the void

  • @arvydas86
    @arvydas862 күн бұрын

    Run first triangle game again, but first random point start in center. What you'll get?

  • @attaulwasay
    @attaulwasayАй бұрын

    Which software did you use to simulate?

  • @aaroncornelison5229
    @aaroncornelison5229Ай бұрын

    What happens in the sierpinski triangle if the initial point selected is in the largest "blank" triangle in the middle somewhere? Would it be the same but with an extra dot where you started?

  • @emeraldnickel

    @emeraldnickel

    Ай бұрын

    Yes - this is demonstrated in a short on this channel.

  • @vyrezbeatz1159
    @vyrezbeatz1159Ай бұрын

    What software is this and can it be used in a DAW like FL Studios. Thank you!

  • @pagezmusic5013
    @pagezmusic5013Ай бұрын

    Make a mandelbrodt set next!!!

  • @thecloudwyrm7966
    @thecloudwyrm79662 ай бұрын

    Interesting. Does the last shape have any sort of name? Great video

  • @AlgoMotion

    @AlgoMotion

    2 ай бұрын

    Not that I know of, just a cool looking fractal! Thanks for watching.

  • @jeffsmith9384

    @jeffsmith9384

    Ай бұрын

    @@AlgoMotion it looks like a fps map

  • @chry003
    @chry00311 күн бұрын

    I tried doing it, but it doesn't work.. Maybe I didn't do it correctly idk.

  • @pistol._.alexxx
    @pistol._.alexxxАй бұрын

    my teacher showed this video in class

  • @legendari-on-yt-you-mfers
    @legendari-on-yt-you-mfersАй бұрын

    Debating using this for music inspo

  • @durimmiziraj4815
    @durimmiziraj4815Ай бұрын

    P5.js? Tell me pls.

  • @loveandoneness.n.e.t
    @loveandoneness.n.e.tАй бұрын

    Is there any correlation between chaos game and cymatics? Seems the organization is similar, in a way

  • @Mareloko41
    @Mareloko41Ай бұрын

    If we could use this to find of song of stars in the night sky that would be awesome

  • @facundomonaco2733
    @facundomonaco2733Ай бұрын

    Does anyone know what kind of app or program is he using for this?

  • @drdca8263

    @drdca8263

    Ай бұрын

    Presumably code he wrote?

  • @96thelycan
    @96thelycanАй бұрын

    i belive if you changed tthe note to be jazz bass samples it would sound really fire

  • @alexrayder1
    @alexrayder1Ай бұрын

    That's interesting but, what is the point of using notes if you're not doing it for scales ?

  • @rvsamsung77
    @rvsamsung77Ай бұрын

    C augmented C-E-A ❤

  • @danielkeller6610

    @danielkeller6610

    Ай бұрын

    C E Ab

  • @Rubygal
    @RubygalАй бұрын

    Look at all the little triangle people

  • @floretionguru2977
    @floretionguru2977Ай бұрын

    Hey AlgoMotion, I also work with music, quaternions and the Sierpiński triangle. We should do a project together.

  • @mcasualjacques
    @mcasualjacquesАй бұрын

    maybe the 3 circle points and the midway process are just using the chaos dots to display 'their' structure/ so it's not as much the chaos initially containing any structure. if the rules were for example non-equilateral placement, the chaos would 'display' the structure of that arrangement. But but maybe we could consider randomness a rule like the others, what happens next you won't believe! Just kidding i don't know what would come out of it. Oh you could use digits of pi or phi to replace random().

  • @mcasualjacques

    @mcasualjacques

    Ай бұрын

    i started writing this in Daz Studio (Qt/Javascript1) charged particles interacting through time so motion. ballz = Scene.findNodeByLabel("ballz"); nodes = ballz.getNodeChildren(); f = new Array() for( i = 0; i { node = nodes[i]; f[i] = Math.random() * 2 - 1; obj = node.getObject() if( obj ) shp = obj.getShape(0) mat = shp.getMaterial( 0 ); if( f[i] mat.setDiffuseColor( Color( "blue" ) ); else mat.setDiffuseColor( Color( "red" ) ); } dsg

  • @mcasualjacques

    @mcasualjacques

    Ай бұрын

    we could say but not really understand "it's not order out of chaos, it's chaos into order or constrained by order, or marshalling chaos or classifying random things like positions (or distances) in the game's domain.

  • @shikaishik
    @shikaishikАй бұрын

    何でこうなるのですかね? あと、中東のマカームをベースに作図したらどうなりますかね?

  • @majorse203
    @majorse2032 ай бұрын

    wowie

  • @PupdudePwns
    @PupdudePwnsАй бұрын

    Sierpinski did the Triforce before it was cool

  • @azid_hsb
    @azid_hsb2 ай бұрын

    Do more bogosort live please?

  • @AlgoMotion

    @AlgoMotion

    2 ай бұрын

    It's live right now!

  • @azid_hsb

    @azid_hsb

    2 ай бұрын

    Okay

  • @joaoericocaldasdelima7735
    @joaoericocaldasdelima7735Ай бұрын

    1º - Suavemente

  • @Fromyoutube640
    @Fromyoutube640Ай бұрын

    1.Sierpiñski triangle 2.Hexagon Chaos Game ...

  • @elbonnieto8929
    @elbonnieto892927 күн бұрын

    7:55 minecraft music disc

  • @titaniumbone5979
    @titaniumbone59792 ай бұрын

    voice reveal?

  • @gbyt034
    @gbyt034Ай бұрын

    at ~0:25 the inside out theme's motif plays

  • @gbyt034

    @gbyt034

    Ай бұрын

    0:23 allows one to hear it in full

  • @Finity2010-ud2rl
    @Finity2010-ud2rl2 күн бұрын

    You're really restrcting yourself by doing these in the Circle Of Fiths. There are plenty of chaos games that are interesting that aren't mutliples of 12.

  • @Bozpot
    @Bozpot10 күн бұрын

    It sounds like Arkenoid.

  • @neopalm2050
    @neopalm2050Ай бұрын

    chaos game is my least favourite way of rendering an IFS, but I guess the better ways can't be easily turned into music.

  • @defitsch
    @defitsch2 ай бұрын

    Has nothing to do with the circle of fifths though. It just depends if you start with an equilateral polygon like triangle, hexagon, etc. It's not the magic of music, as one might think when reading the title ;)

  • @AlgoMotion

    @AlgoMotion

    2 ай бұрын

    The circle of fifths is just being used here as a vehicle for adding *audio* to these well-known fractal visualizations. It facilitates a basic form of *algorithmic composition* of music to accompany the chaos game visuals (algorithmic composition is a common theme on this channel). It should be clear that the circle of fifths is not "producing" the fractals, but rather the fractals are just being superimposed on top of the circle of fifths, merely to add a musical element.

  • @matthewgrabowski9212
    @matthewgrabowski92127 күн бұрын

    If you want a headache watch this video

  • @Mareloko41
    @Mareloko41Ай бұрын

    Did you purposely stayed away from the center?

  • @gfghdgfghd6391

    @gfghdgfghd6391

    Ай бұрын

    The triangle cannot be in the center because of the way the points are oriented

  • @gfghdgfghd6391

    @gfghdgfghd6391

    Ай бұрын

    If you start in the center, there will be 1 dot in the center of the serpenski triangle

  • @gfghdgfghd6391

    @gfghdgfghd6391

    Ай бұрын

    The aspect ratio prevents it from being in the center for the rest of the

  • @bantri256
    @bantri256Ай бұрын

    It sounds, like the Duran Hungry Wolf arpeggio: kzread.info/dash/bejne/qoaDrdqGktavgqQ.html

  • @shredhappy101
    @shredhappy1012 ай бұрын

    The second one sounds almost exactly like Zelda OoT

  • @savonliquide7677
    @savonliquide7677Ай бұрын

    What is the connections with circle of fifth? Except the circle? The notes are not even related to the position or angle inside but only to the random note (and not even the good one) i dont t deny the beauty of maths here (that are not a scoop but ok it is nice) but why underlying lies like wrong links

  • @chaosme1ster

    @chaosme1ster

    Ай бұрын

    The 3 points on a circle producing the Sierpinski triangle (the 1st example in the video) is a well-known mathematical phenomena. The circle of fifths really has nothing to do with it, just as the "halfway" notes are in no way "halfway" between anything and anything. I don't mind though -- I think the fractals still are cool and (for most people) unexpected, and the notes add a fun dimension to watching the video.

  • @Titus2.3-5
    @Titus2.3-5Ай бұрын

    Pretty snowflakes

  • @Vlow52
    @Vlow52Ай бұрын

    Basically, a complicated cherry picking, it works only because of restrictions of an angles you start with. If you would really take it randomly, it would be just a mess.

  • @themichaelconnor42
    @themichaelconnor4222 күн бұрын

    This isn't chaos at all. Your initial limitations are where the structure comes from. It's like dumping a bunch of sand on top of a bucket, then blowing away all the sand until only the bucket remains and saying... Look! Structure from chaos!

  • @isohumulone
    @isohumuloneАй бұрын

    1, Your first point cant be randomly placed. 2. This has nothing to do with the circle of fifths.

  • @QuindaliusBarnacleJonesJr.
    @QuindaliusBarnacleJonesJr.Ай бұрын

    This is kinda cool but it has literally nothing to do with the circle of fifths.

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