Pattern Perception in a Dynamic Universe

Apparent Motion:

Extracting Basin and Sub-basin Patterns
from Dynamic Systems

How might the processes which enable apparent motion be a basis for pattern perception in general?

Do not click on or manipulate the figure at the right, it is only an image. The interactive interface is below.

Instructions

Adjusting your Computer's speed to your Monitor's speed: Most monitors cannot paint accurately faster than 66 to 77 frames per second (fps).

Moreover, apparent motion effects are most robust when stimuli are presented about 25 frames per second (fps).

Delay. When you push the Play button you can click on the Use Delay radio button (highlighted in yellow) and then set the Delay (between iterations) slider (highlighted in yellow) so that the fps indicator (highlighted in violet) falls somewhere between 25 and 66 fps. In that range you should experience apparent motion effects. If your computer is slow, you may not need to use the Speed control.

Clicking on the Delay Slider Bar. To get finer-grain adjustments, you may click on the slider bar for the Delay Control, and the delay will increment (or decrement) a small amount.

Adjusting Window Size. The critical manipulation you will do is adjust the window size. This adjustment sets the phase relations among (1) your perceptual ability to perceive apparent motion/stability, (2) the dynamics of the system, and (3) the representation of those dynamics in a window.

Highlighted in blue on the illustration is the slider bar for adjusting theWindow Size variable. Just drag the slider along the slider bar to increase or decrease the Window Size.

Clicking on the Window Size Slider Bar. To get finer-grain adjustments, you may click on the slider bar for the Window Size Control, and the Window Size will increment (or decrement) one iteration.

Separator Bar. You may want to seem more iterations than the output frame (the part of the applet where you see the black and white squares of the historical trace) shows. You may drag the separator bar (highlighed in orange) to increase the size of the output frame. Or, you may click the little left-pointing arrow (highlighted by an orange oval toward the top of the illustration) to expand the output frame to its maximum size and to hide the control frame. If you do, remember you can click on the little right-pointing arrow to return the output frame to its normal size and to show the control frame.

Perturbing the System. Although not particularly related to the theoretical points we are making here, you may want to perturb the system and examine other basins. The perturb button will do this. The slider bar associated with the Perturb button adjusts the number of nodes whose states are reversed when you click the perturb button. Do not perturb the system until you finish the set of experiments outlined below.

Basic Information about this Dynamic System

We will repeat the figures from the referring page for convenience here

Figure 1. Four highlighted repetitions of a basin of length L=18 in a historical trace of the dynamics of a small system. The system's nodes are the vertical axis and the iterations (time) are the horizontal axis.

Basin Length = 18. This small dynamic system (as first loaded before you perturb it) will have a basin length L=18. Some integer multiples of 18 are 18, 36, 54, 72, 90, ... When you look at the interactive interface, the output should similar to Figure 2

Nodes with Sub-basins of lengths 1, 2, and 3 are also present in the dynamics. First lets find find sub-basins of length 2 (See Figures below).

Finding Basins

Top

Press Play. First: Adjust the speed to between 25 and 66 frames per second as instructed above.The output panel of the interface (left) should show what appears to be a frozen pattern of black and white squares that looks identical (other than the highlighting) to Figure 1, above. In fact is not static but is being painted (on the interface below) at many frames per second (fps). So you are seeing apparent stability.

Explore. Play with Window Size (which is the number of iterations being painted to the screen at any moment). Notice that multiples of 18 produce apparent stability in the dynamics.

Finding Sub-basins

Find Sub-basins Length = 2. Move the slider bar for the Window Size (in iterations) to 70. You will notice that the historical trace of all nodes that have SubL=2 will freeze (apparent stability). Any Window Size that is an integer multiple of 2 will reveal the nodes that have sub-basins of length 2.

Figure 2: Sub-basins of length 2. All nodes (rows) have been dimmed out except those rows that have sub-basins of SubL=2. For the overall basin, the length L=18. The system's nodes are the vertical axis and the iterations (time) are the horizontal axis.

Find Sub-basins Length = 3. Move the slider bar for the Window Size (in iterations) to 69. You will notice that the historical trace of all nodes that have SubL=3 will freeze (apparent stability). Any Window Size that is an integer multiple of 3 will reveal the nodes that have sub-basins of length 3.

Figure 3: Sub-basins of length 3. All nodes (rows) have been dimmed out except those rows that have sub-basins of SubL=3. For the overall basin, the length L=18. The system's nodes are the vertical axis and the iterations (time) are the horizontal axis.

After you play with the specific basin that loaded up, you can press the Pertub button which most likely will shift the system into other basins, which, in this system, are all L=18. But occasionally differences occur in sub-basins.

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