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-[The following note originally appeared on the emusic-l mailing list.  It is
-reprinted here with the author's permission]
-
-From xrjdm@FARSIDE.GSFC.NASA.GOV Wed Nov 23 11:26:39 1994
-Date: Tue, 4 Oct 1994 15:09:23 -0500
-From: Joe McMahon <xrjdm@FARSIDE.GSFC.NASA.GOV>
-Reply to: Electronic Music Discussion List <EMUSIC-L@AMERICAN.EDU>
-To: Multiple recipients of list EMUSIC-L <EMUSIC-L@AMERICAN.EDU>
-Subject: Automata: the long-awaited summary
-
-Back in August, I think, I promised to post a quick intro to cellular
-automata and how they can be used as a sound-generation tool. Since I'm
-going to take a couple of different sources and sum them up with little or
-no direct attribution, combined with my own opinions, I'll give everybody
-my references *first* so they can delete the article and draw their own
-conclusions if they so prefer.
-
-The primary reference that got me started on all this is one in the CMJ:
-Vol 14, No. 4, Winter 1990: "Digital Synthesis of Self-modifying Waveforms
-by Means of Cellular Automata" (Jacques Chareyon). Those who are already
-familiar with automata may just skip to that article and forget about the
-rest of this one.
-Note: the article gives a mail address for M. Chareyon, but he did not
-answer an inquiry about any available recordings using this technique in
-1990.
-
-So. Anyone still here? Good.
-
-Cellular automata are a mathematical concept first introduced in the late
-1940's. Generally speaking, a cellular automaton consists of a grid of
-cells. Each cell may take on any of a number of values - binary automata
-(cell on or cell off) are the most commonly studied. Each cell has a
-neighborhood, defined more simply as other cells which influence its state.
-The exact nature of this influence is defined by what are called transition
-rules. The cellular automaton starts off with some cells in any of the
-allowable states. for each "step" in the automaton's history, the
-neighborhood of every cell is checked, and the state of the cell is
-updated. All updates occur simultaneously.
-
-The transition rule must describe the resulting state of a cell for every
-possible configuration of other cells in the neighborhood. For large
-numbers of states, the amount of memory required to hold the transition
-rule becomes increasingly large, Therefore, some automata use what is known
-as a "totalistic" rule. These rules simply sum the values of the cells in
-the neighborhood and then assign a result on this basis. The resulting
-tables are far smaller.
-
-Many readers may already be familiar with John Horton Conway's game of
-"Life". This is a two-dimensional binary automaton with a totalistic rule.
-This makes for a very small rule set:
-
-  i) If fewer than two filled cells (cells with value 1) surround a cell,
-     it becomes empty next generation.
- ii) If more than three filled cells surround a cell, it becomes empty
-     next generation.
-iii) If exactly three cells filled cells surround a cell, it becomes
-     filled on the next generation.
-
-This corresponds to a totalistic rule set with a total of 8(2-1)+1 or 9
-rules (one each for the sum values of 0 (no cells with a value) through 9
-(all cells with a value) ).If the transition rule were represented as a
-non-totalistic one, the rule set would need 2**8 or 256 entries. There are
-many interesting totalistic automata, so giving up detailed description of
-every nuance of the transitions to save memory space isn't a big sacrifice.
-
-Interesting as two dimensional automata are, they really aren't terribly
-useful for music making. There have been some experiments which have
-attempted to use a two-dimensional automaton to generate MIDI events -
-synthesis at the note level, using :
-
-Battista, T. and M. Giri, 1988. "Composizione Tramite Automi Cellulari."
-Atti del VII Cooloquio di Informatica Musicale. Rome, Italy: Edizione Arti
-Grafiche Ambrosini, pp. 181-182.
-
-Edgar, R. and J. Ryan, 1986. "LINA" Exhibition of the 1986 International
-Computer Music Conference, San Francisco: Computer Music Association.
-
-I have not heard any of the music from these efforts, so I certainly can't
-pass any judgement on them. For the purposes of this summary, we'll just
-look at one-dimensional automata. These use a linear array of cells, with
-the neighborhood generally being one or two cells on either side of each
-cell.
-(This is the type of automaton dealt with in M. Chareyon's article, which I
-will be paraphrasing broadly hereafter).
-
-M. Chareyon's automata are wavetables. A digitized signal is stored as a
-linear array of numbers in memory. A totalistic rule is used to determine a
-lookup value which indexes into an array containing the resulting value;
-this is saved into a second array. After the first array is completely
-processed, the roles of the two are swapped and the process is repeated.
-
-The limiting factor in this process is the number of bits of resolution
-being used to generate the sound. For a totalistic rule using a two-cell
-neighborhood and 12-bit individual samples, we have 3*(2*12) = 12288
-entries in the rule table. At 2 bytes each, this is  24K of storage. If we
-go to 16-bit sample resolution, we have 196608 entries at 2 bytes each for
-a total of 393216 bytes, or 384K.
-
-The key point of M. Charyeon's method is the use of small neighborhoods
-with large numbers of cellular states. Since the computation of the new
-wavetable is all table lookup, very complex transition rules can be
-precomputed and loaded into the tables, allowing the synthesis to
-essentially be a fast sum-and-lookup loop to calculate each new wavesample.
->From the article, it appears that M. Chareyon was able to produce 2 or 3
-voices in realtime on a Mac II with a Digidesign Sound Accelerator board.
-It seems that it would probably be possible to use an AV Mac to do it
-without the board.
-
-This LASy (Linear Automaton Synthesis) method is closely related to the
-Karplus-Strong plucked-string algorithm, in that a wavesample is run
-through an algorithm which recirculates the samples to "self-modify" the
-wave. In fact, a judicious choice of table entries allows one to very
-simply simulate the K-S algoritm directly.
-
-So what are the sounds like? Some automata produce waveforms which quickly
-"ramp-up" to complex spectra and then drop off quickly. Others move to a
-steady state and then remain there. Yet others produce never-ending and
-unpredictable waveforms, whose harmonic content is constantly changing.
-
-Obviously enough, the original wavesample can be obtained mathematically,
-or by actual sampling and using LASy as a waveshaper. As M. Chareyon notes,
-a quick estimate of the number of possible automata for a 2-neighbor
-totalistic rule using a 256-entry wavetable with 12-bit entries is
-(2**12)**256 * (2**12)**(3*2**12) or about 10**4500 possible automata. Of
-course, many, many of these would not be suitable for music (e.g., the 4096
-automata in which all values go to one vlaue in one step, etc.); however,
-the number of musically useful automata is still likely to be an immense
-number.
-
-M. Chareyon provides a number of examples of ways to fill out the rule
-tables and a number of hints on creating wave tables - generally speaking,
-one can create a function which is used to compute the values to be placed
-into the table and then fill it so it can simply be loaded and used by the
-basic algorithm. His experience in using LASy is that he manages
-approximately 50% of the time to produce sounds with the desired
-characteristics, and that about 10% of the remaining time he gets
-unexpected but useful results which can be used as starting points for
-further exploration.
-
-Again, the important point is that the basic automaton uses wavesamples at
-full resolution, calculating a new wavesample for each step of the
-automaton; the next wavesample can be played while the new one is being
-calculated. Because of the large number of states, mathematical tools for
-the analysis of automata and the construction of automata with specifically
-desired qualities require too much storage and compute time to make them
-useful for LASy purposes.
-
-Again, much of this article is paraphrased from M. Chareyon's article; I
-take no credit for any of the work in this note. I'm just summarizing.
-
-The following other articles were referenced by M. Chareyon's article:
-
-Burks, A., ed. 1970. Essays on Cellular Automata. Champaign/Urbana, IL:
-University of Illinois Press.
-
-Chareyon, J. 1988a. "Sound Synthesis and Processing by Means of Linear
-Cellular Automata." Proceedings of the 1988 Internation Computer Music
-Conference. San Francisco: Computer Music Association.
-
-Chareyon, J. 1988b. "Wavetable come Automa Cellulare: una Nuova Tecnica di
-Sintesi." Atti del VII Colloquio di Informatica Musicale, Rome, Italy:
-Edizioni Arti Grafiche Ambrosini, pp. 174-177.
-
-Farmer, D., T. Toffoli, and S. Wolfram, eds. 1984. Cellular Automata.
-North-Holland Physics Publishing. [One of the definitive works on cellular
-automata - fairly heavy math, not a popular presentation - JM]
-
-Gardner, M. 1970. "The Fantastic Combinations of John Conway's New Solitare
-Game 'Life'". Scientific American 223(4) 120-123. [A good introduction to
-cellular automata, focusing on 'life' in specific. Useful intro if my
-1-paragraph summary of automata was confusing :) - JM]
-
- --- Joe M.
-
---
-"At the end of the hour, we'll have information on the sedatives used by
-the artists,,," (MST3K)
-