Stand Alone Smilie

First Example
of Visual Representation of system dynamics using
Twinkling Nodes

The main point here is to show a concrete example of an array of N twinkling nodes (N = 16 in this case) to help with the discussion of the logic underlying N, K Boolean dynamic systems. This is a very small system.

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. Press the Black Double Arrow to move the system forward one iteration at a time.

Just pressing PLAY and STOP is sufficient to visualize what we mean by an array of twinkling nodes in the discussion. But you can anticipate some of the epistemological issues we will eventually be concerned with by doing some of the suggestions noted below.

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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?

Obviously, some nodes stay frozen in one state or the other, that is ON or OFF (1 or 0).

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.

You probably can perceive a pattern in the twinkling but it's not that easy considering that this is such a small system that was choosen for this example because its behavior is very simple. Anticipating what we will explain fully further along in the text we will say that this dynamic system is in a basin that has a length of four (L=4).

Press the PERTURB Button. The system may or may not change to another basin. The basin that the system falls into after being perturbed may have the same length or a different length. Can you find the new pattern? Is it the same or different than the previous pattern? If it is exactly the same pattern, as we shall see in the text of the page that sent you here, then it must be the same basin. How shall we know when a dynamic system changes basins? How can a predator know when the prey has changed its cyclic patterns of visiting the water hole?

Epistemological Questions. Epistemology refers to the processes by which we come to know what we know. Just above, you used your experience to figure out that this system of blinking nodes repeats its configuration every four iterations (we haven't explained what an iteration is in the text discussion yet, but in a discrete system iterations can be thought of as the passage of time). As we develop our ideas about discrete dynamic systems we will explore ways humans can apprehend pattern in massively complex situations. If Kauffman's (1993) arguments in the Origins of Order that the massive simplification implied by a discrete dynamic systems model is actually an interesting and useful way to explore biological phenomena including the origin of life and its subsequent evolution and if Bateson's (1979) eerily parallel arguments in Mind and Nature that all mental phenomena can be reduced to transformations of difference circulating through networks (i.e., discrete dynamics systems) are both taken as useful foundations, then the sort epistemological puzzles, the sort of challenges in pattern perception that we will present to you are a reasonable but abstract approximation of the kinds of knowing that all biological being have had to engage in to make a living and to survive on this planet. We are starting with what appears to be a very simple model but it is one that, it has been argued, encompasses what is important about both mind and nature. The sort of puzzles that you will have to solve with this software and the sort of issues you have to think about to solve those puzzles may well be a useful, albeit abstract, outline of the nature of biological knowledge.

The PERTURB button. The PERTURB button has little effect on what you see in the twinkling nodes. This dynamic system has only 3 known basins and it almost always falls into the same basin. (If you just started reading, what that last sentence means will become clearer as you read more about discrete dynamic systems.)

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 mhz or 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 and then set the Delay (between iterations) slider so that when you push the Play button the ips indicator (next to the Play controls) falls somewhere between 4 and 66 ips. In that range you should get an accurate picture of the behavior of the system.

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

Information about this Dynamic System: Number of nodes, N= 16; Connections per node, K = 3, Self-referencing nodes = 100%, Inline connections to upstream neighbors = 100%. It's wiring is not pseudo-randomly constructed, rather each node receives input from the three neighbors to its right (reading across and down rows as you would in English text). The general characteristics of the pattern of connection among nodes is shown in the figure at right. The truth tables for each node are generated pseudo-randomly. The system has only three known basins and almost always falls into the same basin when perturbed.