Computational Artwork

Where I had been experimenting with just the outsides of the mandelbrot before, I’ve started having a look at modifying the inside of the fractal as well. I’ve continued to use the frequency spectrum for the effects simply because it goes with the frequency spectrum used in the background.

import ddf.minim.*;
import ddf.minim.analysis.*;

FFT fft;

AudioPlayer song;
BeatDetect beat;

float fSize;

void setup()
{
size(300, 300);

// always start Minim first!
Minim.start(this);

// specify 512 for the length of the sample buffers
// the default buffer size is 1024
song = Minim.loadFile("freedom.mp3", 512);
song.play();
beat = new BeatDetect();

float fSize = 20;
// an FFT needs to know how
// long the audio buffers it will be analyzing are
// and also needs to know
// the sample rate of the audio it is analyzing is
fft = new FFT(song.bufferSize(), song.sampleRate());
}

void draw()
{
background(0);
// first perform a forward fft on one of song's buffers
// I'm using the mix buffer
//  but you can use any one you like
fft.forward(song.mix);
fill(255);

loadPixels();

// Maximum number of iterations for each point on the complex plane
float maxiterations = 200;
float xmin = -2.5;
float ymin = -2;
float wh = 2;

beat.detect(song.mix);
if ( beat.isOnset() ) fSize += 0.1;

fSize = constrain(fSize, -10, 10);

ymin = -1;
xmin = -1.5;

maxiterations = maxiterations + fSize;

// x goes from xmin to xmax
float xmax = xmin + wh;
// y goes from ymin to ymax
float ymax = ymin + wh;

// Calculate amount we increment x,y for each pixel
float dx = (xmax - xmin) / (width);
float dy = (ymax - ymin) / (height);

// Start y
float y = ymin;
for(int j = 0; j < height; j++) {
// Start x
float x = xmin;
for(int i = 0;  i < width; i++) {

// Now we test, as we iterate z = z^2 + cm does z tend towards infinity?
float a = x;
float b = y;
int n = 0;
while (n < maxiterations) {
float aa = a * a;
float bb = b * b;
float twoab = 2.0 * a * b;
a = aa - bb + x;
b = twoab + y;
// Infinty in our finite world is simple, let's just consider it 16
if(aa + bb > 16.0f) {
break;         }
n++;
}

// We color each pixel based on how long it takes to get to infinity
// If we never got there, let's pick the color black
if (n == maxiterations) pixels[i+j*width] = 0;
else pixels[i+j*width] = color(n*(song.right.get(i)*50) % 255, n*(song.left.get(i)*50) % 200, n*(song.right.get(i)*30));
x += dx;
}
y += dy;
}
updatePixels();
}

void stop()
{
song.close();
super.stop();
}

In this version I have used the BeatDetect class and another variable, fSize with a constraint on it and then added to the maximum iterations. This allows the frequency spectrum to spread through the mandelbrot fractal, or appear to anyway. It is actually just using the frequency spectrum to colour the fractal, and this makes it appear like spectrum is forming the fractal.

You can have a look at it in action here. The song used in this piece is “Freedom (Waking Mix)” by vo1k1 2008 – Licensed under Creative Commons Attribution Noncommercial (3.0).

This is fairly CPU intensive, so many computers will have trouble running this, it is also about 13mb to load so you probably don’t want to try it on a low speed connection.