## prisma

## licho

## phase 1.2

**phase. (click on the picture to start)**

1.2 – VERTICAL DOTS AND LINES! hold V while clicking or pressing space to generate vertical dots and lines.

1.1 – Now Updated with randomizing tool and some visual effects. Press Z for random dots ON grid and X for random values anywhere.

1.0 – Now updated with possibility to Save/Load sound as a “phase vector”.

Press C to copy the current dots and lines (as a phase vector) to your clipboard. Paste a phase vector in the white box and press [ENTER] to load.

## THE BUTTERFLY EFFECT

The Butterfly Effect is the name of my final course work for ‘Experimentalism, Minimalism and the New Hearing’ that I studied at the Music Department on UCC autumn 2010. Below are some background information and explanation to the experimental music piece.

First some information about the Lorenz attractor, a 3-dimensional dynamical system that the piece is based upon:

**The lorenz attractor** was first studied by Edward Norton Lorenz, a mathematician and meterologist, around 1963. It was derived from a simplified model of convection in the earths atmosphere. It also arises naturally in models of lasers and dynamos. The system is most commonly expressed as 3 coupled non-linear differential equations.

dx / dt = a (y – x)

dy / dt = x (b – z) – y

dz / dt = xy – c z

The series does not form limit cycles nor does it ever reach a steady state. Instead it is an example of deterministic chaos. As with other chaotic systems the Lorenz system is sensitive to the initial conditions, two initial states no matter how close will diverge, usually sooner rather than later.

**The Piece:**

I have written a computer program (in Actionscript 3.0) that generate a number of sine tones proportional (in frequency) to the variables (x,y,z) of the dynamical system as time goes by. At the same time the values of (x,y,z) is plotted on the screen in a visualization of a sound 3D space.

The three variables (x,y,z) in the three differential equations are directly proportional (with same proportions on all of them) to the frequencies of two sine tones each. These two tones are related to each other as a “fifth” (in just scale). So the first tone connected with variable x has frequency p*x and the second one have frequency 1.5*p*x, where p is a proportionality constant. And for reasons I will explain soon the piece consists of TWO systems like this generating sound at the same time, so there are 2*3*2 = 12 tones playing constantly during the piece.

**The Lorenz attractor demonstrates **a famous feature in chaotic systems called the Butterfly Effect which basically means just what I said before about the system being sensitive to initial conditions; “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?”. Moreover, with my setting of parameters a,b, and c in the equations above the 3D plot of the system will always after a while turn into the shape of a butterfly’s wings. BUT it will never stop moving around and the path will differ very much even with small differences in the first values of x,y,z.

To start the piece, the user (or listener) clicks with the mouse somewhere in the sound space to start the piece and at the same time set the initial values (the initial frequencies of the different tones). The two systems are “created” in both visual space and sound space with just a few percentages difference between each other in coordinate values and frequencies.

Then the program plays you the Butterfly Effect, both on the screen and in the loudspeakers (or even preferably; headphones). The piece goes on until the user is satisfied with the butterfly and clicks wherever with the mouse.#

## experiment3

Börjar bli klart tror jag, lite finjusteringar på diverse parametrar kvar men i stort sett kommer det bli såhär:

**obs: **om du hör skrapande och/eller klickande ljud så prova att byt webläsare. Ljudet buggar för mig i Chrome men funkar fint i firefox. Allra bäst resultat får man förmodligen om man laddar ner swf:en och spelar i flashplayer10.

## Hemsida till Apport productions

## experiment1

## raga

Klicka på bilden ELLER om den känns laggig i webbläsarn, ladda ner denna zipfil och läs readme.txt

edit: Har problem att visa denna med chrome. Firefox funkar fint.

## En klocka/musikspelare

Försöker, försöker, försöker lära mig actionscript ordentligt. Är lite meckigt! Klicka på bilden eller här: http://2×4.4×2.net/