Musical Parameter Mappings by 1 Dimensional Cellular Automata

Dave Burraston

Some musical studies, submitted to Wolfram's NKS 2003 conference, consisting of musical parameter mappings created by 1D Cellular Automata (k=2, r=1) of 7 cells. The .ca files were made using Mathematica and contain evolutions of a 7 cell CA from all 128 possible starting conditions. A patch to load the file and create the mappings was constructed using IRCAM Open Music. From this it was possible to select an individual evolution of the chosen 1D CA to produce musical motifs by mapping these individual evolutions to musical parameters as specified in the filename :

n = note number

o = note onset time

d = note duration

v = note velocity

Partial screen shot of patch made in Open Music to convert CA data to MIDI (Above)

In the filenames below the number suffix indicates the 1D CA initial conditions for these parameters. The results are presented as single channel MIDI files for open interpretation in your MIDI application and 256k mp3 synthetic audio renderings made at the Creativity and Cognition Studios, Sydney. The program has the ability to map a CA to a MIDI channel, using the Modulus function to limit the number of channels between 1 or 16.

The animated gifs and quicktime movies are a visual representation of the CA values. Each frame displays the CA evolution for each of the 128 possible starting conditions.

NOTE : Onset times and durations are mapped to millisecond values so some scaling of the CA output was applied as indicated.

Rule 110
Rule 45
Rule 150
Rule 225
r110-7bitallx64.mov r45-7bitallx64bmp.mov r150-7bitallx64.mov r225-7bitx64bmp.mov
r110-all7bit-65gens.ca r45-all7bit-65gens.ca r150-all7bit-65gens.ca r225-all7bit-65gens.ca
Onset Time x 2, Note Duration x 8 (mp3 rendered at 5bpm) Onset Time x 2, Note Duration x 8 (mp3 rendered at 7bpm) Onset Time x 2, Note Duration x 8 (mp3 rendered at 30bpm) Onset Time x 2, Note Duration x 8 (mp3 rendered at 10bpm)
r110-n16o8d4v2.mid

r110-n16o8d4v2.mp3

r45-n16o8d4v2.mid

r45-n16o8d4v2.mp3

r150-n16o8d4v2.mid

r150-n16o8d4v2.mp3

r225-n16o8d4v2.mid

r225-n16o8d4v2.mp3

r110-n1o3d5v7.mid

r110-n1o3d5v7.mp3

r45-n1o3d5v7.mid

r45-n1o3d5v7.mp3

r150-n1o3d5v7.mid

r150-n1o3d5v7.mp3

r225-n1o3d5v7.mid

r225-n1o3d5v7.mp3

r110-n2o4d8v16.mid

r110-n2o4d8v16.mp3

r45-n2o4d8v16.mid

r45-n2o4d8v16.mp3

r150-n2o4d8v16.mid

r150-n2o4d8v16.mp3

r225-n2o4d8v16.mid

r225-n2o4d8v16.mp3

r110-n7o5d3v1.mid

r110-n7o5d3v1.mp3

r45-n7o5d3v1.mid

r45-n7o5d3v1.mp3

r150-n7o5d3v1.mid

r150-n7o5d3v1.mp3

r225-n7o5d3v1.mid

r225-n7o5d3v1.mp3

Onset Time x 3, Note Duration x 8
r110-n16o10d11v12.mid
r110-n16o16d16v16.mid
r110-n16o17d18v19.mid
r110-n16o1d2v3.mid
r110-n16o32d64v96.mid
r110-n16o4d5v6.mid
r110-n16o7d8v9.mid


Selection of BOE fields constructed in DDLab and musical visualisations with equivelent mappings of initial conditions for each Rule (Onset Time x 2, Note Duration x 8), n=16, o=8, d=4, v=2.

Rule 110 file r110-n16o8d4v2.mid


Rule 45 file r45-n16o8d4v2.mid


Rule 150 file r150-n16o8d4v2.mid


Rule 225 file r225-n16o8d4v2.mid


Rule 45 file r45-n16o8d4v2.mid (close up of duration overlay)


Rules and Regulations ~ The Bit Player

Serendipitous Selection of Computational Sublimity

A brief sample of interesting examples from the testing phase.

MIDI files
SSCS0.mid SSCS1.mid SSCS2.mid SSCS3.mid SSCS4.mid
SSCS5.mid SSCS6.mid SSCS7.mid SSCS8.mid SSCS9.mid
mp3 audio files
SSCS10.mp3 SSCS11.mp3 SSCS12.mp3 SSCS12a.mp3 SSCS14.mp3
SSCS15.mp3 SSCS16.mp3 SSCS17.mp3