Oscillators Rule


The parent of this page is: Cool Universes in the Cosmos of Cellular Automata

Oscillators Rule is a universe among the 2-D totalistic cellular automata, defined by S1235/B45, where random patterns shrink to tiny oscillators, with periods anywhere between 1 ("still lives") and 16. Larger periods are rare. All the contents of figure 1, below, resulted from an initial rectangle covering the entire figure, that was randomly-filled with cells. Click on the figure to see it in action.

Figure 1. Oscillators in the universe "Oscillators Rule" (Click on the figure)

(If you are not already familiar with how to interact with our figures, please note that you can start/stop the figure by clicking once on it, and reset it to its original configuration by dragging with your mouse anywhere on its surface.)

The colors of the oscillators are indicative of their period. For a full explanation of our color-coding, read this page of ours. Generally, if an oscillator has period less than 16, our program shows it with a color other than red; otherwise, it is shown as red. Since there is no (pure) red spot in figure 1, we conclude that all oscillators shown have periods less than 16. Can you make an oscillator with greater period?

So let's have some hands-on activity. Below, we present our program as a full-featured applet with its normal interface. You won't click and drag on this applet to interact with it; instead, you can click the buttons on its toolbar (top), and look at its status-bar (bottom) for some information. Although we hope the interface is self-explanatory, this page of ours describes it in more detail. Now, what to do with it? Please read the information that follows.

Here is our suggestion for what to do with the program, above. Move your mouse close to the upper-left corner in the black space, click and hold it clicked down, then drag it somewhere close to the bottom-right corner of the space, and finally release the button of the mouse. You'll see a white rectangle being formed while you drag the mouse. This is your "selection rectangle". You can do a number of things with this selection rectangle, all of which are possible if you click once on it. Go ahead, click once anywhere within the selection rectangle. You'll see a menu popping up, with one of its buttons in the middle saying: "Fill with random cells" and a percentage (50%) right next to it. Click on this button. You'll see the selection rectangle being filled randomly with red cells. Finally, click on the "play" button (), sit back and watch.

After 32 epochs the program will freeze for a short time, examining whether any portions of the space have stabilized (to oscillators or still lives). It will then continue running for another 32 epochs, at which point it will momentarily freeze again, checking for stable parts. This run-and-examine mode will continue a few more times, until everything in the space has turned into an oscillator (or still life). From that point on the program will run uniterrupted, simply rolling the oscillators. Try to see if there is any red oscillator, that is, one with a higher period. You can measure its period by pausing the program first (), then noticing one of its "faces" (that you could recognize later) and using the "step" button () to see after how many steps it comes back to the face that you recognize.

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