Iannis Xenakis and Cellular Automata - D Burraston
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The following summary was originally
presented in (Burraston 2006), and has a few additions.The architect/composer Iannis Xenakis, one of Olivier Messiaen's
students, is probably the most famous artist to have used CA in composition
practice. His interest was based on the simplicity of the CA process to produce
a rich output (Varga 1996). Xenakis used CA calculated with his "pocket
computer" to determine the succession of chords within a rational, perceptible
structure for sections of his orchestral composition Horos in 1986.
Xenakis
may have used CA in several other compositions before his death in 2001, although
the complete extent of his application is still unknown. Xenakis (1992) states in the preface of
his book "Formalized Music" that the use of CA "can be found
in works of mine such as Ata, Horos, etc.
Greater detail on the CA used in Horos and the mapping process can be found in (Hoffmann 2002,
Solomos 2005), where it is shown that Xenakis applied the output to bars 10,
14-15, 16-18 and 67-71. Mapping to musical output was based
on pre-determined pitches and the state of the cell chose the instrumentation.
The presence or absence of cells controlled the musical events. Xenakis was also quite
happy to interfere with the output as he saw fit. The approach taken utilised
a 5 state totalistic nearest neighbour (v5k3) automaton of one dimension and
three different rules. The first rule used was 20041042004105 and
this is said to be derived from rule 42004105 in Wolfram's Scientific
American article (Wolfram 1984b). It should be noted that these two rules
are not exactly the same, the differences in their behaviour
can be seen in Fig 2.16 (top left and right). The other two rules are given
by Solomos are 22414105
and 20404105 and were used in a mixed form, examples of spacetime
behaviour is shown in Fig 2.16 (bottom left and right).
Fig 2.16 Rule 42004105
from Wolfram's Scientific American article (top left). Rule 20041042004105
(top right), 22414105 (bottom left) and 20404105 (bottom
right) used by Xenakis in Horos.
Xenakis may have used fixed rather than periodic boundary conditions.
It
is difficult to ascertain precisely from these papers how the CA used by Xenakis
implemented the boundary. The importance of specifying the type of boundary
conditions was stated by Wuensche and Lesser (1992), if they are fixed the
system will become more disordered, because the wiring is atypical at edge
locations. he type of boundary conditions one chooses will depend on the application
or investigation requirements. Solomos (2005) states : 1) the far right column of cells "does not
intervene in next line calculations" and 2) the handwritten annotations
on the far left column are "manually added by Xenakis". This seems
to imply that the right column boundary is fixed at null (0). The other options
are choosing a fixed state value between 1 and 4. It is not clear whether
the handwritten left column is a manually added part of the CA calculation,
or added arbitrarily and not part of this calculation.
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Fig 2.17 Close up of XenakisÕ
text/symbol pocket computer printout for Horos (left) presented in Solomos
(2005). The same rule, 20041042004105 with 23 cells and periodic
boundary, viewed as graphic blocks and stretched to line up with printout (right).
A close up of Xenakis pocket computer text/symbol printout presented
in Solomos (2005) is shown in Fig 2.17 (left). The printout shows 22 printed
columns of cells and hand annotations creating an extra column on the left.
The same rule, 20041042004105 with 23 cells and periodic boundary,
is shown as graphic blocks in Fig 2.17 (right). Comparing the pocket computer
printout with the data it can be seen that differences occur at timestep 12
as the CA reaches its boundaries. Note that this rule will evolve to
all 0's (single cycle attractor) with periodic boundary conditions for a system
size of 22 or 23 cells from a single seed. A discrepancy arises in the spacetime
evolution depicted in Fig 1 of Hoffmann's '2002) paper, as that shows a 21
cell system. Solomos (2005) examined more of Xenakis scores between 1986 and
1990, suggesting that a further 8 pieces may have used CA in some way.