TECHNOLOGY
Here, I would like to give you an outline of GCM; Globally Coupled Map Chaos [1]. Firstly, let us think of something called chaos-generator. For general example, let me give you a logistic map as: X(n+1)=1-αX(n) 2 As you can see through the form of this equation, the Chaos is supposed to be obtained when the former output is to go to the input of next step. Here, I have prepared plural Chaos-generators like this, take an average of the each output, and let the value have feed-back to the input of the each chaos-generator. A conduct of X(i),which is the "i"-th chaos-generator when there are number of N Chaos-generators, is expressed as the equation bellow:
Ｘn+1(ｉ)=(1-ε)ｆ(Ｘn(ｉ) )+(ε/N)Σｆ(Ｘn( j ))
j
However,in this condition, f(x)=1-αX2 Fig.1 shows the model above. Two parameters which conflict with each other are existing in this model. One is "α", given the strength of chaos from each chaos-generator,and the other is " ε", given the strength of combination with the whole average. In this model, even if these two chaos-generators take very close values, soon the difference between these two will become bigger, because chaos has sensitive dependence on initial condition, as its basic characteristic. This characteristic leads a phase of chaos-generator's oscillation to be scattered. On the other hand, the combination with the average tends to work toward the direction which makes the oscillation of chaos-generator even. Actually, when you calculate this equation with changing these two parameters, you will obtain the results as: if "ε", the strength of the globally coupled is bigger, each Chaos-generator will lead to a condition that each of them oscillates totally shutting itself up which is called as Coherent phase. On the contrary, if "α", the strength of the chaos is bigger, the oscillation of each Chaos-generator will become a totally scattered condition desynchronized phase. In this point, it is interesting to see the middle conditions Ordered phase and Partially ordered phase . Especially,in the case of Partially ordered phase, chaos-generators shutting themselves up and vibrating are going to separate into some clusters, and the chaos-generators in each cluster come to oscillate in phase, though the phase, amplitude and period of the oscillation will be different in every cluster. Moreover, each cluster once collapses as the time passes, then those chaos-generators will make several new clusters again later on. However, in this second time it is not always to happen that the same chaos make clusters which have the same construction before. The phenomena that the clusters are going to be systematized, be collapsed and make another clusters, is called as "chaotic itenerancy".
[Fig1] Globally coupled map
"Ping-Bang" is a multimedia performance work. The title "ping-bang" is consist of double meanings words.The word "Ping" is a famous Unix command to confirm the computers connection. And the "bang" means that a kind of triggering command of musical language "MAX". As you know from the usual meanings of title ,some explosion scenes and sounds to imagine them are used in it.it's realized by some connected Macintosh computers .
"Ping-Bang" is a multimedia performance work. Hence I will mainly discuss about its music and performanc part. "Ping-Bang" is a solo performance work for MIBURI *1 which is a Yamaha's new type physical modeling synthesizer. All the sound in this work is generate in real time (without tape and sequencer) and some visual part is controled by performer with MIBURI. Fig 2. shows a blockdiagram. Performance datafrom MIBURI is sent out as MIDI signals. And they are input to a Macintosh computer for preprocessing its huge MIDI raw data. And next preprocessed MIDI data are send to the Macintosh. The PowerBook180 executing the GCM algorithm. We will describe how the GCM algorithm applied for this work. "Ping-Bang" is consisted on 3parts, we called them, A part,Bpart and C part. Acompanyment parts of B and C part use the GCM algorithm. Their part is consist of solo part played by MIBURI and accompanyment part of GCM algorithm which is controled by MIBURI(computer assisted accompanyment part). The GCM algorithm used in this work has 16 Chaos-generators.Each Chaos-generator's output is assigned 16 musical instrument's parts of multi-timbral synthesizer(TG77) in use of 16 MIDI channels. At the B part, we assign the 16 chaos generator to 4 for drums ,4 for percussions, 6 for percussive sounds, 1 for sustain sound and 1 for bass. At the C part, 4 for drums ,2 for percussions, 5 for percussive sounds, 4 for sustain sound and 1 for bass. All the chaos generator's outputs are converted to integer by linear conversion and assigned MIDI note number. At the drum and percussion sound, MIDI note number doesn't represent the pitch but the specific drum instrument. SO that its output control the kind of percussion or drum instruments. And these output value control the rithm of each sound by selecting the note length.Bigger value makes short length note.
Please remenber that previous section. GCM algorithm is controled by two parameters ("α" and "ε"). In this work,Different "α" is given to each chaos generator by randam function.MIBURI performer control the parameter "ε" by MIBURI's MIDI OUT. I assigned shoulder bend data to control "ε". When the performer hold up hands ,we can get the maximum "ε".So performer control the GCM by up and down the hands.This means that performer can control the all accompanyment part by shoulder.
The author would like to thank prof. K.Kaneko and the students in his lab. for introducing GCM algorithm to me and sharing important discussions.
[1]K.Kaneko :"Clustering, Coding, Switching,Hierarchical Ordering, and Control in Network of Chaotic Elements", Physica 41D,P137-(1990)
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