Second Example of Twinkling Nodes

This second example of a discrete dynamic system is is more complex than the first example. Like the first example it has an array of N=16 twinkling nodes. To see the nodes twinkle, first press the USE DELAY radio button first and then press the green PLAY arrow. The nodes will go on and off. We've taken the convention that light green indicates ON and dark green indicates OFF. If the nodes are turning on and off too slowly, use the Delay Slider to reduce the delay (increase the speed) or, even, turn the Delay off by clicking the Delay radio button again. Press the red STOP button to stop the dynamics.

Just pressing PLAY and STOP is sufficient to visualize what we mean by an array of twinkling nodes in the discussion. But can you apprehend the patterns in the twinkling of the nodes? Can you at least discern what the basin length of a particular pattern is?

Press your browser's Back button to return to the text.

Can you find a pattern in the twinkling? Set the Delay Slider so that the nodes are twinkling at a rate that you like. Is there a pattern across time? That is, does the configuration of which lights are on and off (which changes with time) eventually repeat itself?

You can press STOP and then press the black DOUBLE ARROW which moves the system its next configuration. Press the black DOUBLE ARROW several times and you will probably notice that the system repeats configurations every four times you press the back DOUBLE ARROW button.

When the applet starts running for the first time, it is in a basin of length 18 (L=18). That is, you have to press the black DOUBLE ARROW 18 times before the configuration of on ON and OFF nodes repeats itself.

Epistemologocally, extracting the dynamic pattern in the twinkling nodes when it is 18 iterations long is challenging. Yet we will demonstrate elsewhere on this website that human neurology prosesses characteristics that make extracting such patterns (including this one) rather easy under certain conditions. What those conditions are has revealing implications for the nature of human knowledge.

More Puzzles. You can press the PERTURB botton on the interface. That will provoke the dynamic system to enter another of its basins. Can you perceive a new pattern if you perturb the system? As a start, you might attempt to determine how many times you have to push the black DOUBLE ARROW before the configuration of nodes repeats. At least then you would know the basin length of the new basin. Of course, knowing how long the basin is is not the same as comprehended the pattern in the flow changes in the twinkling lights.

As a hint to at least finding the basin length of any new patterns you provoke by pressing the PERTURB button, this dynamic system has 36 known basins and their lenghts are factors of 6.

NOTE: This applet has controls for detecting basins through sound, but THEY ARE NOT CONNECTED. THE SOUND DOES NOT WORK. But, even saying that the sound is not connected implies that it might. Other applets will demonstrate the power of sound sequences in detecting dynamic patterns.