Do not click on or manipulate the figure at the right, it is only an image. The interactive interface is below.Pattern Perception in a Dynamic Universe
Exemplar 3 Applet
Layered Waves of Motion
CITATION: Malloy, T.E., Butner, J., & Jensen, G. C. (In Press). The emergence of dynamic form through phase relations in dynamic systems. Nonlinear Dynamics, Psychology, and Life Sciences.
Contents
Instructions
Basic Information about this System
What to look for when you run the Simulation
Interactive Simulation: Layered Waves of Motion
Do not click on or manipulate the figure at the right, it is only an image. The interactive interface is below.
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).
Use Delay. Before (or after) you start the system by pressing Play, click 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 around 35 fps. Near 35 fps you should experience the particular apparent motion effects we discuss below. If your computer is slow it may not be able to paint 35 frames to the screen in one second because of the large number of nodes (horizontal axis). In that case reduce the Window Size, W.
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) one msec.
On the right side of the output frame is a purple scroll bar. Use it to scroll down so that the system dynamics fill the entire output frame. [Notice in the image above, the purple scroll bar on the right is pulled all the way down.] Top
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 the Window 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 see as many as 100 iterations, but the output frame (the part of the applet where you see the black and white squares of the historical trace) does not show that many iterations. You may drag the separator bar (highlighted 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
Basins. In one application of the TAO Tool to this discrete dynamic system we found 200 basins in 200 perturbations of the system. Every basin was of length L = 200 iterations. This means that apparent stability of the whole pattern will occur only in multiples of window size W = 200. Since our interface only allows a Window Size of up to 200, setting W = 200 is the only option for apparently stabilizing the whole pattern generated by the ongoing dynamics of this system.
Sub-basins. There are no known sub basins of this system.
What to Look for when you run this Dynamic System
The image at the left shows an example of output from the dynamic system when
the system is stopped. Notice that the purple scroll bar on the right side is
dragged down so that the output fills the entire output frame. Notice also that
one of several wave like forms has been highlighted in yellow. In a similar
way, one of the patterns composed of vertical white bars is highlighted in blue.
After you adjust your speed to 35-37 fps: Press Play and look at the output panel of the interface. The interaction of your visual system with that output might well produce the experience of a surface of waves moving right to left with a background moving down and to the right.
Just what the surface waves look like depend on how you focus your visual system. Try focusing on the output in different ways.
Layered Emergent Dynamic Patterns. It may be possible to see either the patterns highlighted in yellow or in blue moving right to left.
What is important is that layers of moving pattern emerge. They appear to be layered in depth and move across each other in different directions and at different rates. The proposal is that these dynamic layers are co-constructed by your visual neurology and the flow of a dynamic system.
Abstract Dynamic Patterns. The moving (dynamic) patterns you perceive are abstract in their form and are being generated by the ongoing flow of an abstract logic. They are not meant to "look like" anything. The general conjecture that we make is that these layered dynamics emerge in a way that meaningful forms emerge in everyday life.
Where and When. These emergent patterns are not cycles or sub-cycles of the attractor. That is, there is no single row (node) whose frequency corresponds to these waves. Rather, these patterns exist within capsules of time; they exist on some iterations (horizontal axis) but not on others. They exist in an intersection of where (the output of certain nodes as represented on the vertical axis) and when (certain iterations).
On this page, we will focus on the perceptual dynamics apparent in the neighborhood of 35 fps.
You may explore your experience of other perceptual effects by adjusting the delay (between iterations) so the output varies from around 25 frames per second (where apparent motion effects begin) up to 66 frames per second where your monitor may begin to produce irregular and unpredictable contributions to the perceptual dynamics you perceive.
The default Window Size for this applet is 91; so you are looking at patterns that emerge for the phase relations (among the system dynamics, the size of the frame being painted on the screen 35 times a second and your nervous system) that result from a window size of 91. There are many more patterns of interest for different window sizes.
Dynamic Simulation and Suggested Experiments (see text below simulation interface)
Adjust your speed to 35-37 fps by clicking the Use Delay radio button and clicking on the Delay bar.
The perceptual effects we discuss are extremely sensitive to how fast the computer is painting to the screen (fps). You will see different things entirely if you change the speed to, say, 25 fps. If your computer is slow it may not be able to paint 35 frames to the screen in one second because of the large number of nodes (horizontal axis). In that case reduce the Window Size, W.
This speed effect is well known in apparent motion but is not addressed in this paper.
Experiments with Window Size (fps = 35)
Window Size = 88. Use the Window Size slider bar to the right of Slider Control to get a Window Size = 88,
Now notice that at Window Size = 88 the the layered dynamics simplify. It is easier to perceive the movement of the yellow-highlighted waves (in this case from left to right).
Window Size = 100--Apparent Stability. Click on the slider bar and move Window Size up to 100. Here we perceive islands of apparent stability against a pulsing background. These islands of apparent stability are in no way static--they are produced by the flow of the system dynamics interacting with that part of a human visual system that produces the cluster of apparent motion effects
Window Size = 99 & 101. Click the slide bar to adjust Window Size to 99.
Notice that at these window sizes, the stable islands of pattern move coherently together either left to right (W = 99) or right to left (W = 101).
Conjecture: The set of window sizes (99, 100, 101) and its effects on perception evoke the possibility of how human visual neurology might interact with a dynamic universe to produce objects that appear to be static (W = 100) or objects that have coherent movement (W = 99, 101).
Explore. Play with Window Size (which is the number of iterations being painted to the screen at any moment). There are many interesting dynamic patterns which emerge. These patterns never exist across all iterations for any one node; rather, they exist only for some itertions and not for others.
Perturb. You can perturb the system and explore the many other basins that this dynamic system falls into for perceptual effects.