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
4:52 its amazing how similar this sounds to Chamber of Sages from Legend of Zelda.
@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
Ай бұрын
Haha thought the same thing g
@baefaux
Ай бұрын
It even looks a bit like the chamber of sages from top down too
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
Played the video too loud and my furniture started to levitate. And I think I opened a portal.
9:00: Coltrane is jealous.
Me trying to do every combination lock to get in my brothers phone:
i love fractals
Why is 0.789 used on the dodecahedron fractal?
Must be what Spielberg was thinking b4 he made close encounters
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
That is more the result of the chosen method rather than something to do with notes and music.
Chaos Within Structure = Structure Within Chaos
i just listened to fractals for so long
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?
When are you releasing on spotify
Super cool channel man!
Its nice you doing other sort of content!
Beautiful
2:25 *insert Zelda chest opening theme here*
Why was 0.789 used for the Dodecahedron? Curious to look further into it
Great video
1:35 The sound is like c418 - cat
The sounds are satisfying
So cool! Like a treasure hunt.
Algomotion voice jumpscare???
3:25 fractal sounds.. awesome 😎
7:01 Now *that* is what I call, the Koch Hexagram!
Sumamente interesante, saludos desde uruguay
THE TRIFORCE IS REAL!
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?
But this is true for any triangle, why the circle of fifths?
It’s the trifor
@HalfBreadOrder
Ай бұрын
y
Sounds like hitting the jackpot on a slot machine, or so ive heard 😂
The dodecagon is super cool
What if you select a dot inside of the void
Run first triangle game again, but first random point start in center. What you'll get?
Which software did you use to simulate?
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
Ай бұрын
Yes - this is demonstrated in a short on this channel.
What software is this and can it be used in a DAW like FL Studios. Thank you!
Make a mandelbrodt set next!!!
Interesting. Does the last shape have any sort of name? Great video
@AlgoMotion
2 ай бұрын
Not that I know of, just a cool looking fractal! Thanks for watching.
@jeffsmith9384
Ай бұрын
@@AlgoMotion it looks like a fps map
I tried doing it, but it doesn't work.. Maybe I didn't do it correctly idk.
my teacher showed this video in class
Debating using this for music inspo
P5.js? Tell me pls.
Is there any correlation between chaos game and cymatics? Seems the organization is similar, in a way
If we could use this to find of song of stars in the night sky that would be awesome
Does anyone know what kind of app or program is he using for this?
@drdca8263
Ай бұрын
Presumably code he wrote?
i belive if you changed tthe note to be jazz bass samples it would sound really fire
That's interesting but, what is the point of using notes if you're not doing it for scales ?
C augmented C-E-A ❤
@danielkeller6610
Ай бұрын
C E Ab
Look at all the little triangle people
Hey AlgoMotion, I also work with music, quaternions and the Sierpiński triangle. We should do a project together.
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
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
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.
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?
wowie
Sierpinski did the Triforce before it was cool
Do more bogosort live please?
@AlgoMotion
2 ай бұрын
It's live right now!
@azid_hsb
2 ай бұрын
Okay
1º - Suavemente
1.Sierpiñski triangle 2.Hexagon Chaos Game ...
7:55 minecraft music disc
voice reveal?
at ~0:25 the inside out theme's motif plays
@gbyt034
Ай бұрын
0:23 allows one to hear it in full
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.
It sounds like Arkenoid.
chaos game is my least favourite way of rendering an IFS, but I guess the better ways can't be easily turned into music.
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
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.
If you want a headache watch this video
Did you purposely stayed away from the center?
@gfghdgfghd6391
Ай бұрын
The triangle cannot be in the center because of the way the points are oriented
@gfghdgfghd6391
Ай бұрын
If you start in the center, there will be 1 dot in the center of the serpenski triangle
@gfghdgfghd6391
Ай бұрын
The aspect ratio prevents it from being in the center for the rest of the
It sounds, like the Duran Hungry Wolf arpeggio: kzread.info/dash/bejne/qoaDrdqGktavgqQ.html
The second one sounds almost exactly like Zelda OoT
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
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.
Pretty snowflakes
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.
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!
1, Your first point cant be randomly placed. 2. This has nothing to do with the circle of fifths.
This is kinda cool but it has literally nothing to do with the circle of fifths.