Linked Oscillations

These are not the influence coupled oscillations of physics and biology: Huygens pendulum clocks or southeast Asian fireflies. Our oscillators are logical circuits ( a closed circuit with an odd number of inversions) which are directly linked logically. They do not necessarily oscillate periodically but can wait indefinitely to complete an oscillation.

The movie illustrates the oscillation linking behavior which will transition its output to red only when both inputs are red and will transition its output to blue only when both inputs are blue. When the inputs are different the linking behavior will hold its output and wait for both inputs to be the same. Since both oscillations monotonically transition between red and blue it is guaranteed that red completeness will always occur and that blue completeness will always occur and that the linked oscillations will oscillate in synchrony indefinitely.

In the movie one oscillation is faster than the other and waits on the slower at the linking behavior.

A series of linked oscillators form a spontaneously flowing pipeline in which emerges a  path through which flows stable wavefronts of red and blue.

The stable flow path, which we will call the flow path, through the linked oscillations is highlighted below as the black path which flows from left to right . The grey paths flowing from right to left with the inversion, closes each oscillation around its link behavior and will be called the closure path. Below that the pipeline of oscillations is redrawn to emphasize the path of stable wavefront flow which is the straight path through the middle.

flow path

The movie below illustrates the behavior of the redrawn structure of linked oscillations

The demonstration below is a series of linked oscillations forming a pipeline through which transitioning colors flow.  The pipeline has 3 variable speed oscillations: one at the input, one at the output and one in the middle of the pipeline. Each oscillator oscillates between red and blue through a single point of color inversion. Oscillators are linked through a completeness behavior with the completeness logic red & red and blue & blue. When both inputs to the linking behavior are the same color the color passes through the behavior and each oscillation progresses. Play with the speeds and get familiar with the adaptive behavior of the logically determined pipeline. Notice how each oscillation waits indefinitely on linking completeness to complete its oscillation. Green is start and red is stop.
(this requires Flash and does not work in Safari)

This a pipeline of linked oscillations in the form of the redrawn structure above making it easier to observe the flow path. The big red dots are the oscillation links and the little black dots are the flowing  transitions.

The sliders left, mid and right control delays in the left most, right most and middle oscillations respectively. The slider hide is a toggle that will hide the closure flow and show only the data path flow through the pipeline. Play with the delays and oabserve hot the delays affect the flow path and how they interact with each other.

The Data – NULL/Empty  Convention
We designate the two different conditions as data and null representing them in the movies as red and blue respectively. Now we can speak in terms of data values and null values and in terms of stable wavefronts of data values spontaneously flowing through a background of all null emptiness. Each transition to data followed by transition to null is a data wavefront flowing through a background of null. It has a leading boundary rising out of the emptiness and a trailing boundary sinking back into the emptiness.

Symbolic data such as numbers can be integrated into the oscillation flow behavior. The linking completeness behaviors can be interaction behaviors such as arithmetic functions. The structure of linked oscillations can be a complex network of flow relations through which wavefronts of data spontaneously flow and compute.