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View Full Version : Fractals. Let's have 'em!


Brad
2006-01-30, 16:24
I'm writing a few little programs to help me with a music composition class I'm taking for fun this semester. My current favorite is one that reads in MIDI files and generate a series of notes and durations based on patterns in those songs. I'm not satisfied, though, and am looking for something a little more interesting.

Enter my hair-brained scheme to involve fractals.

:)

Now, honestly, I'm a bit green when it comes to the mathematical approach to fractals. I know the basics of fractal geometry that we all learned in grade school like Pascal's Triangles and such. You take a pattern and you repeat it over various sections recursively.

How does this work with ranges/sequences of numbers? Are there specific programming techniques used to generate fractal data? Iterative or recursive? Are there particular algorithms that have to be followed or can one just "make up" a fractal that works? What resources should I investigate as a "Fractals for Dummies" sort of guide? Don't tell me to Google it; most results are fairly worthless. :p

In case it matters, I'm using Java so I don't have to write my own helper functions to manually extract the MIDI data.

If I do manage to produce a piece of music that is more than just "academic" and sounds moderately pleasing, I'll be sure to share it with you all. No promises, though! Most computer-generated music that I've studied generally sounds like total junk to Joe Sixpack. It may not be any time soon, too, because this is supposed to be a semester-long project.

Brad
2006-01-30, 16:44
Don't tell me to Google it; most results are fairly worthless. :p
Mmm. Crow sure tastes good this time of year.

I found one page that actually fits perfectly with what I intended to develop. This guy explains the basics of some fractal algorithms he's used: Fractal Music (http://www.geocities.com/SiliconValley/Haven/4386/algorith.html) And, of course, he generously provides all his source code. Awesome!

I'd still like to know more about the theory, especially if any of the resident developers or mathemagicians have experience with fractals and number theory like this.

billybobsky
2006-01-30, 18:39
I did a presentation in college on the Tent Map, which is perhaps the simplest non-integer dimention function known... It's bifurcation diagram is very pretty (http://upload.wikimedia.org/wikipedia/commons/3/3a/TentMap_BifurcationDiagram.png).

Edit: bah!

curiousuburb
2006-01-31, 07:29
Well... there's MIDIfier (http://www.oddible.com/projects/midifyweb/), which takes (web or standalone) text and makes it music... also available as a standalone app (OS X port coming) (http://www.knzaudio.com/index.php)

Both sound like the first component of your plan... as for the fractal math part...

Spanky's page (http://spanky.triumf.ca/www/whats-new.html) at the TRIUMF particle accelerator under UBC has plenty of links, as does Paul Lee's... (http://home.att.net/~Paul.N.Lee/Fractal_Software.html)including various software links, math functions and software reference links. There are also some OS X (http://www.sticksoftware.com/gallery.html) tools (http://www.fractaldomains.com/) among the links on the pages above.

For a simple visual guide to "which equation gives what looking complex fractal" see Dickau's page (http://mathforum.org/advanced/robertd/index.html) of Mathematica stuff.

Or check out Fractal of the day (http://home.att.net/~Fractals_3/FotD_06-01-31.html), complete with the parameter file and formula code under each image.