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Plugging outputs back into inputs yields chaos.

Brief Explanation

The previous page let you plot a point whose coordinates were determined by the preceding point. That is an example of the general concept of recursion or feedback. Sound engineers have struggled, and musicians have used, this phenomenon. Here is how you hook it up:

audio feedback

If you have ever done this, you know what it sounds like. A quieter example is video feedback: when you point a camera at its own display screen:

video feedback

Try It Yourself

Here are the results of carrying out the experiment pictured above. As the camera twists, you can see the (delayed) response of the screen. If there were no delay at all, the video feedback would be a lot less interesting: just an infinitely-receding tunnel.

(If the embedded video does not play, click here for the YouTube version.)


Artists have used this concept for many years. Below is a cartoon by Charles Addams, that inserts a devilish twist in the multiple-mirror idea. Look close at the series of reflections. Actually seeing this would be pretty scary!


The next pages will let you explore simple (and not-so-simple!) examples of taking the output of a mathematical function and re-applying the function to it.

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