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| Autonomous
Collective |
| Gödel Trilogy |
These
compositions were recorded between 1997 and 2001 using techniques based
on mathematical, chaos and complexity algorithms with generative software
manipulation tools. These systems were initially prototyped on Acorn machines
using the BASIC programming language. Apple machines running Max were
used in the later stages. The algorithms were drawn from (among others)
1 and 2 dimensional Cellular Automata, Lorenz and other strange attractors,
various mathematical functions of 1 to 3 dimensions, 1/f Voss noise generator,
Logistic equation. This research was done informally and detailed notes
will be presented on current work as it progresses. The compositional
process in general followed these steps :
Select and code algorithm
Test and experiment with different mappings on various synthesizers :
CA controlling chaotic events
CA and Chaotic sequences
CA sequences juxtaposed with chaotic modulations
CA sequences and mathematical functions
CA sequences juxtaposed with manual keyboard playing
CA sequences and reassembled percussion
CA controlling chaotic events and modulating synthetic formant generator
Capture/Render MIDI data to sequencer / Capture audio to sequencer
Edit algorithmic MIDI and audio if required
Add non algorithmic elements if required
Final Arrangement
Short videos of data generation (from Frax-Mix)
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2
dimensional mathematical function x=sin(A)*cos((0.01*A)) y=(0.5*cos(A))*cos(A*1.95) with values of A from 0 incrementing by 0.05 Used for note, velocity and modulation of synthesis parameters |
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Lorenz
Attractor 3 dimensional chaotic function dx/dt
= ay-ax Used for note, velocity and modulation of synthesis parameters |
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2
dimensional cellular automata - CA The grid of cells is viewed as being infinite. This automata uses a simple rule set of randomized integers and the 2D grid is also seeded randomly. Patterns evolving from this structure are extracted and then used to sequence MIDI synthesizers. |
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Another 2D CA |
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2D Mathematical Functions used as value generators. Here an X and Y function forms the basis for note and control values, for the purpose of synthesis and sequencing. |
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Equipotential lines method of the Mandelbrot Set. This is a very interesting route for plotting the set and extracting control values, compared to the Level Set Method. The shape of the set is drawn out following the boundaries. In this example a unit circle is drawn and a portion of the set is plotted. |
Minerva Attractor (Self referential paradox)
This algorithm was presented in The Philosophical Computer by Grim, P. and with some et. al.in : Self reference and paradox in two and three dimensions, Comput. & Graphics Vol 17, No. 5. p609-612, 1993
It is based on the statement "This sentence is False" :
Y : Sentence X is True
and in 3 dimensions Grim states this as :
Xn+1 = 1-(0.5*(Yn-Zn)-Xn)
Yn+1 = 1-(0.5*(Xn+1-Zn)-Yn)
Zn+1 = 1-(0.5*(Xn+1-Yn+1)-Zn)
Screen shots of test program created at Noyzelab, allowing generation of arbitrary length data sequences and verifying output of BASIC program.
Screen
shot of program created at Noyzelab, allowing generation of arbitrary
length data sequences.
<---related bryen telko performance
Minerva Attractor data table views x, y and z :
Logistic Map
The
1 dimensional Logistic Map, also know as the quadratic or Feigenbaum
map, is a simple iterative function.
Xn+1=AX(B-X)
A=-0 to 4
B=.01 to 1
Xo= 0.01 to 1
The main method of control for a function of this type is to vary A
and keep B at 1. This results in the generation of number sequences
in a controllable range exhibiting structural properties from stable/oscillating
to complex/chaotic. Particularly interesting event sequences can be
constructed by moving between bifurcation points. Pretty much any book
on chaos theory will have something on this.
1/f noise
Stochastic
composition by the use of 1/f noise for the determination of musical
parameters is a method pioneered by Iannis Xenakis with the Stochastic
Music Program in the 60's and 70's.
1/f noise is commonly found in nature being exhibited by nerve membranes,
sunspot activity, River Nile flood levels and most types of music. A
classic scientific paper on this subject -
1/f noise in music:Music from 1/f noise, Richard F. Voss and John Clarke,
J. Acoustical Soc. Am. 63(1) : P258 - 263, 1978
A very popular paper was published by Martin Gardner in Scientific American
1978, 238(4) : P16-32
Selection of stills from the MIDI data
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