Dynamical Systems and Fractals: Computer Graphics by Karl-Heinz Becker

By Karl-Heinz Becker

This examine of chaos, fractals and intricate dynamics is meant for somebody conversant in pcs. whereas preserving the math to an easy point with few formulation, the reader is brought to a space of present clinical learn that used to be scarcely attainable until eventually the supply of desktops. The e-book is split into major components; the 1st offers the main attention-grabbing difficulties, each one with an answer in a working laptop or computer application structure. quite a few workouts let the reader to behavior his or her personal experimental paintings. the second one half presents pattern courses for particular computer and working structures; info seek advice from IBM-PC with MS-DOS and Turbo-Pascal, UNIX 42BSD with Berkeley Pascal and C. different implementations of the photos workouts are given for the Apple Macintosh, Apple IIE and IIGS and Atari ST.

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Extra info for Dynamical Systems and Fractals: Computer Graphics Experiments with Pascal

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After about 30 iterations the program stops. From the 20th iteration on we see these numbers over and over again: . . 7012, . . etc. 5. The attractor is thus the set of those function values which emerge after a sufficiently large number of iterations. 2-2 is called a strange attractor. In the region k > 3 there is just the attractor -00. Whenever a function has several attractors, new questions are raised: . Which regions of the kq-plane belong to which attractor? That is, with which value p must I start, so that I am certain to reach a given objective - such as landing on the attractor l?

It carries out the same tedious, stupid calculation over and over again, always using the same formula. When we go on to write a program in Pascal, it will be useful for more than just this problem. We construct it so that we can use large parts of it in other problems. N e w programs will be developed from this one, in which parts are inserted or removed. W e just have to make sure that they fit together properly (see Chapter 11). For this problem we have developed a Pascal program, in which only the main part of the problem is solved.

It is quicker. It is harder to describe these astonishing pictures than it is to produce them slowly on the screen. What for small k converges so regularly to the number 1, cannot continue to do so for larger values of k because of the increased growth-rate. The We have discovered this curve splits into two branches, then 4, then 8, 16, and so on. effect of 2, 4, or more branches (limiting values) by graphical iteration. 7). 570 we see behaviour that can only be described by a new concept: chaos.

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