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**John
Whitney, Sr. "Notes on Permutations"**

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Originally published in

Film CultureNo. 53-54-55 (Spring, 1972), p. 78

Now to illustrate, in some detail, what I might call visual harmonics. These 281 points are moving about the screen according to a set of instructions in a graphics program which were input to the computer. Incidentally, it would be difficult to find a better demonstration of the powers of the computer as an animation tool than this film sequence. Imagine having to animate by hand 281 points, all moving in precise orbits at independent rates and directions. The program instructions say, in effect: Starting at the center of the screen, step to the right a computed distance and move in an arc around to the left so many computed angular degrees and place one point. From there, compute a new radius distance outward and a new theta arc around and place another point. Now, repeat this procedure again and again for a total of 281 points. This takes about a second or two computation time on the computer to produce only one frame of this motion picture. Each frame is slightly different because some of the parameters of the instruction equation are changing with each new computer picture. As you watch the picture on the screen here, 24 new pictures a second are displayed and you can see changes taking place sometimes very rapidly and sometimes quite slowly. This rate is determined by the size of the incremental steps, or the parametric changes, as they are written into the basic equation. Now you will notice that the points seem to be scattered around in a circular area randomly at one moment. But at certain moments they all seem to fall in line to make up some simple rose curve, symmetrical figure; sometimes it is a three lobed figure, or ten or four or two lobed figure. These action sequences proceeding from order to disorder and back to ordered patterning, suggest a parallel to harmonic phenomena of the musical scale. In an aesthetic sense, they have the same effect; the tensional effects of consonance and dissonance. The scattered points fall into some ordered symmetrical figure when all the numerical values of the equation reach some integer or whole number set of ratios. The effect is to subtly generate and resolve tension - which is similar to the primary emotional power of music composition.

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