4-Node Standard Example
Representation: Historical Trace (Smilie3)
Instructions

By this time you've analyzed intellectually the basin structure created by the flow of logical relations in the system named 4-Node Standard. You've also (probably) looked ath how that flow might be represented by observing the twinkling patterns of the four nodes. The text of the Tutorial page (in the Representation section) explained how Smilie3 represents the dynamics of a system by leaving a historical trace of the flow of state vectors.

This applet allows you to run Smilie3 and examine how these historical traces allow you to extract the dynamic patterns of the 4-Node Standard system. You can compare your experience in extracting pattern using Smilie3 with your experience using the twinking nodes.

Detailed instructions are below. FIRSTclick the DELAY button. Then press the green PLAY button. The Smilie3 output should move across the screen, left to right, each column showing a state vector. As the historical trace gets longer, a repetitive visual pattern will form reflecting the structure of the basin that 4-Node Standard is in. STOP the system (Red button) after observing the historical trace for a bit.

Adjusting Speed. You may want to set the delay between iterations (using the slider) until you get the output moving across the screen at a rate you like (generally around 20 ips).

Window Size. Because the system will run forever and the screen is finite, we have to decide how many itertions we want to see. This is done by setting the window size with a slider bar. When the output of the system gets to the (end of the window (i.e., to its rightmost edge), it will go back and start writing at the begining of the window (i.e., at its left edge). It will write over the output that is already there.

Since the basin length is L=4, if your window sixe is a factor of 4, Smilie3 will overwrite the historical trace with exactly the same trace and you will not see any evidence of over-righting. That is not ideal for observing how Smilie3 works, so it is best to adjust the window size.

Adjusting Window Size. I recommend adjusting window size to a factor of 3 (since basin length is L=4). This will make sure that the output

Perturbing the System. With the speed adjusted, and the window size adjusted to a factor of 3, and the system running, click the Perturb button.

The system may or may not leap to another basin. If it does, which basin is it? How do you know?

Being able to detect basin shifts in a dynamic ecology is a fundamental epistemological puzzle. So too is being able to recognize old basins (or to recognize that a new basin has occurred).

This is a very simple system and we shall in the future study systems with a great deal of complexity. But even in this simple system it is apparent that how the flow of relationship is represented is fundamentally important to extracting pattern.

For your convenience is checking your perceptions of which basin is occurring and when below is the image used to relate the structure of 4-Node Standard to the Smilie3 in the tutorial

Instructions Top

Window Size (iterations). [BLUE HIGHLIGHTS].

This is the most important control conceptually because it adjusts the phase relations between basin length and the processing of the basin (and this allows the extraction of different aspects of the dynamic patterns portrayed here.

Drag the Slider (highlighted in blue) from its default setting of 60 down to whatever size is suggested above for using the particular applet you are viewing. In this case the slider has been dragged down to 11 iterations.

Click the Slider Bar. Optionally you may click on the Slider Bar and the Window Size will slowly scroll in the direction (to right of slider or to the left of slider) you want. You can easily get a change of one unit by clicking on the slider bar. This gives you a finer degree of control over window size than does dragging the slider.

Read the Window Size. To the right of the Window Size area is a number (highlighted in blue) that tells you exactly what the Window Size is. Top

Setting Delay. [YELLOW HIGHLIGHTS].

WHY?: Adjusting your Computer's speed to your Monitor's speed: Most monitors cannot paint accurately faster than 66 to 77 times per second. In this class dynamic systems, we ask the computer to paint each iteration of the system to the screen. Depending on the how fast your computer is (it's clock speed mega-Hz or giga-Hz and what type of video card it has) this software may send requests to paint images 1000 or more times per second. Once the iterations per second is higher that 65 or 70 iterations per second (ips) what you see on the screen is some undetermined interaction between your monitor hardware and the behavior of the dynamic system. In other words, you aren't seeing the behavior of the system any more, you are seeing that part of the behavior that the screen happens to capture.

Solution. Click on the Use Speed radio button (highlighted in yellow). Then drag the Delay (between iterations) Slider (highlighted in yellow) from its (very slow) 250 millisecond delay between iterations down to some lower value that gives you a good sense of dynamic motion in the output. As we said, you generally want the the iterations per second (ips) to between 20 ips and 60 ips, although it seems to work well in this case as low as 6 to 8 ips. You your judgment as this is about your perception.

If your computer is slow, you may not need to use the Speed control. Top

Iterations per Second (ips). [HIGHLIGHTED IN LAVENDER].

When you push PLAY, you generally want to have the iterations per second indicator (just to the left of the double black arrow on the control bar) to be between 20 and 60 ips. This range allows you to perceive apparent motion effects but is within your monitor's ability to paint the screen. Obtaining this range may require setting the delay (see below) between iterations.

One Iteration Forward Button.

Sometimes it is useful for finding pattern to move the system forward one iteration at a time. The double black arrow (next to the green Play button) moves the system forward one iteration each time you click it.

Perturbing the System. [HIGHLIGHTED IN GREEN].

Perturb Button. Perturbation of a system by changing the states of one or more nodes might (or might not) shift the system to a different basin. The Perturb button will pseudo-randomly change the state of given percentage of nodes. The percentage of nodes perturbed is selected by the user.

Slider. The slider (highlighted in green) allows you to select what percentage from, 0 to 100, of the nodes will have their state changed pseudo-randomly. The exact percentage chosen by the user is indicated (green highlight) to the right of the slider scale.

Note that any unconnected nodes (the top thirty nodes in the image) will pseudo-randomly change their values (white to black or black to white) when the Perturb button is pressed. Because they are unconnected, their changes of value will have not effect on the system. Top

Sizing the Viewing Area. [ORANGE HIGHLIGHTS].

Resize Viewing Area. [ORANGE HIGHLIGHTS]. The dimpled bar between the Controls and the Output Frame (Viewing Area) can be dragged in either direction (as indicated by black arrows). This allows you to adjust the viewing area to see more or less TAO levels.

Full-Interface Viewing Area. [ORANGE HIGHLIGHTS (Top)]. Once you have the controls set as you like them you can eliminate them and see more derivatives by clicking on the little left-pointing arrow at the top of the bar dividing the controls from the output frame. Clicking the right-point arrow will return the controls to view. You can also grab the dividing bar and drag one way are another to size the parts of the interface the way you want.

Pseudo-Randomness. This is a deterministic system and therefore probability is not a concept that applies to its behavior. So it is worth noting that the pseudo-random changes that are part of some functions (e.g., perturb button) are deterministic, although so irregular as to fit human perception of randomness (which is a probability concept).

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