By Sebastian Brock
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Additional info for A syriac life of Saint Maximus the Confessor
See R. Abraham, Simulation of cascades by video feedback, in: “Structural Stability, the Theory of Catastrophes, and Applications in the Sciences”, P. ), Lecture Notes in Mathematics vol. 525, 1976, 10–14, Springer-Verlag, Berlin. 3 NTSC is typically 30 frames per second at 480 lines per image. 4 J. P. Crutchfield, Space-time dynamics in video feedback, Physica 10D (1984) 229–245. 20 1 The Backbone of Fractals Monitor Inside Monitor Inside … Effect of long distance between camera and monitor. Basic setup and mapping principle (left), real feedback — monitor inside monitor (right).
3 Basic Types of Feedback Processes This is an algorithm which produces sequences of integers in a most simple way, but yet its unfolding is still not completely understood. Here is the original formulation due to Lothar Collatz: Step 1 : Choose an arbitrary positive integer A. Step 2: If A = 1, then STOP. Step 3: If A is even, then replace A by A/2 and go to step 2. Step 4: If A is odd, then replace A by 3A + 1 and go to step 2. Let us try a few choices for A : 3,10, 5, 16, 8, 4, 2, 1, STOP 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, STOP 75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1, STOP The obvious conjecture is the following: the algorithm comes to a stop no matter what the initial A is.
From what has been said so far, we would expect that in the rotated position we would eventually observe just a sequence of rotated images. But this prediction is far too simple. All kinds of peculiar effects occur due to many different characteristics innate to television image production. For example, the process of scanning the image on the monitor and in the camera is one of sequentially putting together a series of lines to compose the image. There is also the memory effect of the phosphorus on the monitor tube.
A syriac life of Saint Maximus the Confessor by Sebastian Brock