Posts Tagged ‘Fractal’

Fractalesque

Thursday, November 6th, 2008

Done with Quartz Composer with the intention of replicating the appearance of a Fractal Flame rendered through Scott Draves’ Flam3, except live rendered based on audio input.

This isn’t a fractal, but I think it does re-create the appearance quite well.

The video quality isn’t even close to the live render quality, but it gives you a good idea of it.

The screen recording here has taken the mic input and used it for the animation. The song used in this recording is “August (Reggae Rework)” by el-B from http://ccmixter.org/files/elB/16075 under a Creative Commons Attribution Noncommercial 3.0 License.

You can download the Quartz file here, note though that while this will open in Tiger, it will not render correctly, OS X 10.5 Leopard is required for it to run correctly.

It should also be noted that the video above was rendered on a Macbook Pro with an Intel Core 2 Duo 2.4ghz with 2gb of RAM and an 8600m GT and it averages 5 frames per second, so to really experience the full potential of this, it needs to run on a Mac with a fairly powerful video card like a Mac Pro, the iMac’s and new Macbook Pro’s should also render it quite nicely.

The reason it is so intensive is because there are a number of iterator and replicate in space patches along with LFO’s and interpolator’s that are affected by both the audio volume peak and the audio spectrum, so depending on the volume and the type of music, the visualisation develops more variation.

Mandelbrot Player

Wednesday, November 5th, 2008

The mandelbrot before audio playback commencesI’ve built on my previous Frequency Mandelbrot to add basic audio playback controls to it. It no longer starts automatically upon loading, you now have to press ‘P‘ on your keyboard to begin playback and there are a number of other hot keys for different playback options.

An audio file can be played, paused, rewound, and fast-forwarded. The left and right audio channels as well as beats and the overall volume are taken and used to colour a mandelbrot fractal. The left and right audio channels generate a series of lines that change speed and direction based on the audio peaks. The centre of the fractal has a constraint on it based on the beats, so as the amount of beats increase, it will freeze and stay still while the outer area of the fractal, which appears as a background continues to animate around it. And yes, it is meant to have the lines through it.

The keyboard controls for playback are:

Play: P
Pause: S
Fast-Forward: F
Rewind: R
Restart: H
Stop: Q

Mandelbrot during audio playbackA note on these playback options, at the moment, ‘Q‘ will actually close the link to the song file, so this should not be used unless it is needed. Attempting to start the song again with ‘P‘ after ‘Q‘ has been used will cause Processing to error. I haven’t gotten around this as of yet unfortunately.

To replay a song from the start, press ‘H‘ and this will return the play head to the start of the file.

Rewind ‘R‘ and fast forward ‘F‘ skip the track back and forward by 500 milliseconds, so ‘R‘ should be used in place of ‘H‘ if you don’t want to return to the start of the song.

The source code is a little bit different to previous versions as I have added a class for keyPressed to determine what to do if the control keys are pressed:


// Create the controls.
void keyPressed()
{
if ( key == 'p' ) song.play(); // Press P to play the song.
if ( key == 's' ) song.pause(); // Press S to pause playing.
if ( key == 'h' ) song.rewind(); // Press H to reset to the start.
if ( key == 'f' ) song.skip(500); // Press F to fast forward.
if ( key == 'r' ) song.skip(-500); // Press R to rewind.
if ( key == 'q' ) song.close(); // Press Q to quit playing.
}

It’s all fairly straight forward, the Minim library is very simple to use and there are some great tools in it that you can play with. I highly recommend it if you are working with audio in Processing.

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 9mb to load so you probably don’t want to try it on a low speed connection.

The full source code is available from the same page as the applet, or you can see it after the jump:

(more…)

Frequency Mandelbrot

Sunday, September 21st, 2008

Frequency Mandelbrot 1Where 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();
}

Frequency Mandelbrot 2In 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.

Using The Output of Minim in Processing

Wednesday, September 17th, 2008

After following the quick start guide on the Minim website, I put together a little waveform generator that produces a waveform for the left and right channels based on the input of an audio file along with a frequency spectrum running over the top of it. The instructions are pretty easy to follow, and the additional functionality of Minim seems fairly simply to harness to do something useful with.

Minim Output 4I’ve since taken the code from that guide and combined it with a mandelbrot fractal from the Processing tutorials and references. At the moment, the mandelbrot doesn’t really do anything near like what I want it to do, but I am making some progress in figuring out what I can do with Minim and how I can use it for what I want to do.

Initially I took the frequency spectrum and used it to colour parts of the mandelbrot. To start with I only manipulated the red colouring of the fractal to see what would happen which gave me this (you may need to scroll to the right in some places sorry):

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

AudioPlayer song;
FFT fft;

float xmin = -2.5;
float ymin = -2;
float wh = 4;

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("song.mp3", 512);
song.play();

// 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);

loadPixels();

// Maximum number of iterations for each point on the complex plane
int maxiterations = 200;

// 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;  // Bail
}
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*16 % 200, n*16 % 100);
x += dx;
}
y += dy;
}
updatePixels();
}

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

To make the above work, you’ll need to put an MP3 or Wav audio file in a “data” directory within the sketch folder for this sketch and change song.mp3 to the name of your audio file. You can see 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).

Minim Output 5aIt will run a series of lines of various lengths and thicknesses at varying speeds based on the input of the audio file.

Considering how cool this was looking, I decided to add the left audio channel for the green colouring to see what would happened, so I modified the colouring to the following:

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*16 % 100);

Minim Output 5cThis is actually really cool, if you run an audio track through it that has a distinctively different left and right channel you get much more variation in the colouring and it appears to be synced more with the music.

If you try the above, you’ll get reds coming through for the right channel, greens coming through for the left and yellows where they overlap. Since you have two different sets of lines, you can see them change with each channel, rather than only with one channel, this is why it seems to be synced up better, and the colour changes help with this since the colours match the left and right mix. You can see 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).

Adding the second colouring control in also makes colour variations immediately around the main parts of the mandelbrot more prominent, and as they change it makes the fractal appear to be behaving like it is encircled with flames.

Minim Output 7aThis does make the background blue though rather than grey which I don’t like too much since the fractal doesn’t stand out as much with the blue background as it did grey.

I decided to change the colouring again slightly, this time using the audio mix to control the blue colouring. I used the right audio channel again, no particular reason really. So this is what my colouring looks like now:

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));

Minim Output 7e
Minim Output 7c

You can see 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 has the same left and right channel variation and effects as the previous version, but it changes the colours slightly, the lines are now variations or predominately green and purple with a black background. This makes the mandelbrot stand out much more than before, but it also makes the appearance of flames around the fractal much more prominent as they are now blue closest to the fractal and shades of purple the further out you go. This looks really cool and makes the flames even more realistic (except for the colouring of course) and the flames now appear to reach out further making them stand and their variations stand out more.

The Koch Curve Fractal

Thursday, August 21st, 2008

Yesterday in the KKB211 lecture, we briefly went over fractals, in particular the Koch Curve fractal which is probably one of the more well known fractals along with the mandelbrot (Benoit Mandelbrot coined the term fractal).

For anyone that doesn’t know what a fractal is, it is effectively a geometric image that repeats itself infinitely no matter how far in you zoom. They are usually irregular appearing images, but they are “self-similar”.

The koch is a snowflake star shape and is one of the earliest fractal shapes to be recognised.

For an interesting look at how it replicates as you zoom in and how self-similar it is, have a look at the Java applet over at ArcyTech.