Pattern Perception in a Dynamic Universe
Apparent Motion/Stability:
Extracting Emergent Patterns
from Dynamic Systems
How might the processes which enable apparent motion be a basis for pattern perception in general?
Contents
Instructions
Information about Exemplar 2
Extracting Patterns Emerging in Time
Do not click on or manipulate the figure (below, 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).
Delay. Once you start the system by pressing Play, 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) one msec.
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 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 (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 the Exemplar 2 Dynamic System
We will repeat the figures from the referring page for convenience here as well as add new material.
Basins. Exemplar 2 has three known basins, one with length L=50 (our primary focus) and two with L=4. In one sample of 10,000 perturbations, the relative frequency of the basin with L=50 was .6985, the relative frequency of the first basin with L=4 was .3009, and the relative frequency of the second L=4 basin was .0006.
Sub-basins. The basin of L=50 has no sub-basins. That means that (other than window sizes that are a factor of 50) no row (expressing the dynamics of a single node) ever freezes up. The first, relatively more frequent L=4 basin, has sub-basins of length SubL=2. The third basin has never been observed (its existence was determined analytically by the TAO Tool).
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| Figure 1. Historical Trace from second exemplar. Figure shows two cycles of a basin of length L=50. There are no sub-basins in the standard sense. A rich set of complex patterns, some stable, others dynamic, emerge from adjusting the phase relations between Window Size and the system's dynamics. |
Figure 1 shows 100 iterations from the basin with length L=50 as a historical trace. It has no sub-basins, but a rich set of patterns, both dynamic and stable, emerge as the phase relations between system dynamics and window size is adjusted.
Some of these patterns are hinted at in the static snapshot shown in Figure 1, but most are not, especially the dynamic ones. The emergence of such regularity that is not tied to components of the system (nodes) poses serious difficulties for the attempts of measure a physical system to find defining characteristics of the experienced percept. The sort of dynamic patterns that can be extracted in many cases have little to do with the static representation of the behavior of individual nodes shown in Figure 1.
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| Figure 2. 100 iterations of a basin with L=4 from Exemplar 2. This basin has sub-basins of length SubL=2. |
Extracting Patterns Emerging in Time
Press Play. First: Adjust the speed to around 25 frames per second. Surely keep it below 66 frames per second as instructed above.
After you adjust your speed to 25 fps: The output panel of the interface (left) should show what appears to be a pulsing matrix surrounding stable islands of pattern. These islands are mostly black, but some aspects are white. (The pusling matrix a dynamic pattern as well.)
These emergent patterns are not sub-basins in the usual sense. That is, there is no single row that is completely static across all iterations.
Where and When. 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).
The default Window Size for this applet is 75; so you are looking at patterns that emerge for the phase relations that result from a window size of 75. There are many more patterns of interest for different window sizes.
Window Size = 76. Click on the Window Size slider bar to the right of Slider Control. Window Size should jump up to 76. (Get a Window Size = 76 however you can.)
Now notice that at Window Size = 76 the the islands begin move to the left. Have they changed shape? (You can go back and forth between Window Sizes 76 and 75 to answer that question.)
Forward Flow and Backward Flow. Take a pen and let your eyes follow it as you drag it across the screen back and forth, right and left on top of the dynamic pattern. Change the speed with which you move the pen. (The arrow from the mouse works almost as well as a pen tip.) Notice that as your eyes focus on the tip of the pen to the right you will see a dynamic pattersn moving in that direction (You may have to adjust the speed of movement of the pen tip.) Notice, conversely, that as your eyes focus on the tip of the pen to the left you will see a dynamic pattersn moving in that direction also.
Where do any of these patterns go when you press Stop? (Press Play again.) These patterns exist in the dynamics of the system as it unfolds over time. They can't be found in any static aspect of the system. How is that like the perceptual qualities of a rapids as a kayaker wends through them?
Window Size = 77. Click on the slider bar and move Window Size up one notch to 77. What are the changes?
Two Directions at Once. With the system running focus your attention on row five counting down from the top of the black and white output. It is lined up with the red hash mark (indicating the fifth row from the top). Start at the left side and run a pen tip (or mouse arrow) to the right along that row fairly rapidly. Do the black squares seem to flow to the right when you do? (You may have to adjust how fast you run your pen pointto the righ; in fact it may take a little practicet.) Now reverse directions. Run your pointer to the left along the fifth row. Do the black squares now seem to move left? It seems easier to see the squares move left than right; but the rightward movement can be learned. What's it mean for our perception of dynamic systems that direction of movment can shift relatively?
Window Size = 83. Click the slide bar to adjust Window Size to 83.
Run a pen across the screen both right and left. Notice what patterns emerge as you do so and how they are different for the two directions. After you use a pen for a while, notice how you can get some of these patterns, for both directins, simply by moving your eyes.
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.
Some patterns are easier to see if you use a very long delay between iterations resulting in a very slow rate of presentation around 4 or 5 fps.
Finding Basin Patterns. You can find the basin patterns in the usual way by setting the Window Size to a multiple of 50 (50, 100, 150, 200).
Perturb. You can perturb the system and explore the one rather simple and uninteresting basin that you are likely to find, if you wish. Just push the Perturb button a few times.
For the reader's convenience we include below the Discussion and Conclusion section from the Apparent Motin web page:
Discussion and Conclusions
We live in world of complex dynamic patterns whose perception is fundamentally tied to motion. Even that which appears stable is stable only relative to motion.
Physiological Nystagmus. [Note 3 ] Visually static objects in everyday life require the constant movement of our eyes (physiological nystagmus) in order to be seen. Physiological nystagmus is produced by tremors in the eye muscles. These tremors prevent the light from stable objects from falling on the same retinal cells from moment to moment. They do that by shifting the eye less than one degree of visual angle (which is about the distance between two foveal cones) around 10 times a second. Experiments with stabilized images (see Palmer, 1999, p. 521ff) indicate that if an image moves synchronously with these tremors, the perception of that image disappears after a few seconds. Bateson (1979, pp. 90, 91) uses nystagmus as a fundamental example in arguing that difference is the basis of mental process. A static relation between a static object and a static eye would produce no differences and therefore no knowledge; this is in full concordance with the stabilized image results. The perception disappears under such circumstances. Nystagmus assures that the eye receives a continuous flow of differences from environmentally static objects.
Enacting a World, Enacting a Mind. We are proposing that the universe be conceived of as a web of dynamic relations some of which set up a field of dynamic relations on the neural receptors of the retina. This, however, is not a passive receiving, as the word "receptors" taken in its strongest sense might connote. A living being has eye muscles that actively twitch the eyes (nystagmus) so as to create motion relative to the context in which it is enmeshed. Add to this other actions (e.g., saccades and micro-saccades). All these actions, taken in relations to a dynamic universe, co-create the retinal image. That is, the image is not simply received from the world by the eye; the eye (i.e., the being) is an active partner in creating the retinal image. What emerges is a model of dynamically active eyes enacting a receptive field on the retina in relation to dynamic relations ongoing in the universe. Varela, Thompson and Rosch (1993, p. 9) put it this way: "We propose the term enactive to emphasize the growing conviction that cognition is ... the enactment of a world and a mind on the basis of ... actions that a being in the world performs."
What is proposed here is a more general and macro hypothesis than those relating to physiological nystagmus, saccades, and micro-saccades, though those phenomena form a basis for the structure of the model. The proposal is about what happens after the retinal image is enacted. The proposal is that there is a mechanism that can adjust phase relations between the dynamics of the retinal image and the ultimate representation as experienced. That is, we are proposing that a fundamental mechanism of pattern perception is the ability to create and adjust phase relations. Nystagmus is simply an early example of this that influences the retinal image itself. Nystagmus adjusts the phase relations among the firing of neurons in relation to a stationary object. Nystagmus assures that what see as a stable object is "apparent stability" as we have defined it. That is, nystagmus creates a periodic motion in the retinal image at a rate of about 10 frames (in our terms) per second. That fact that it is such objects are seen as stable is not explainable by nystagmus since it is creating change not stability. The fact that such objects are perceived as stable means that somewhere in the system another mechanism has adjusted phase relations so that of the moving retinal image is experienced as "apparently stable." But is is a minor example of apparent stability, macro patterns are also extracted from the retinal image. Let's discuss those cases.
In our experiments we have given explicit control to people so that they could change the phase relations between the dynamics of a simulated universe and its representation. We are proposing that in an analogous way phase relation adjustment might occur between the retinal image and experienced representation. We found that adjusting such phase relations produced striking examples of the extraction of patterns. There were a least three different kinds of such pattern extractions--basins, sub-basins, and emergent, dynamic patterns encapsulated in time.
We propose that the neural system has a mechanism that performs adjustments of phase relations as fundamental process for pattern perception. We do not propose that the neural system has spatially defined "windows" whose size can be adjusted. Rather we propose (that since what our "windows" did was adjust phase relations) that the neural system has mechanism that can and do adjust phase relations so that patterns that could exist on the retinal image actually do come to exist. What do we mean by that? We mean that if we take a static image, see Figure 11, from Exemplar 2, we cannot discern the images we later perceive by dynamically adjusting phase relations (e.g., window size = 75, 77, 83). Those patterns emerge through the action of adjusting phase relations. In a similar way, we propose that a retinal pattern of simulation, supposing we could photograph it, would not show that patterns that a being experiences. Rather, the patterns that a being perceives are, in part at least, due to processes that shift phase relations between retinal image and representation in way a similar to the way that our window size adjustments changed phase relations. [Note 4]
Computational Level Analysis Revisited. Why does human (and perhaps other) neurology enable the "illusion" of apparent motion? Did evolution teleologically aim for movies and video games? Obviously (to us) not. We propose that the illusion of apparent motion is possible because it is based on neural mechanisms which routinely adjust the kind of phase relations that exist in apparent motion experiments and that are the basis of a broad (yet unspecified) range of dynamic pattern perception phenomena.
What and Why. In David Marr's terms, we want to specify the what and why of our proposed pattern perception mechanism. As we stated above, a being needs to be able extract many distinct dynamic patterns at once. Some of these are spatially coherent, others are spread out spatially. Some are unmoving and stable, others are spatially disconnected flows of movement (like hints of a current though a rapids mostly obscured but appearing here and there in the visual field of the kayaker). How do we form coherent patterns from these fragmented dynamics on the retina?
Computational Constraints. We began this web page with some broad constraints for a mechanism for the extraction of dynamic pattern. For various reasons we would like our proposed mechanism to be able to extract patterns of motion that are not spatially adjacent. We would also like to be able to shift between different patterns of motion. In our example, these spatially separated patterns of motion may be a collective like a herd or a single coherent object, say a deer, that is masked by something irregular like leaves. In short a useful requirement is that a coherent pattern does not have to be coherently adjacent on the retinal image. The experiments with the window size mechanism demonstrate the power of phase relation adjustments in extracting patterns with these general constraints.
A second design constraint we mentioned at the outset is that there be a way of distinguishing dynamic patterns, that there be a way of highlighting one dynamic pattern and then shifting to another dynamic pattern and highlighting it, or, even better, a way of having multiple highlights each pointing at different dynamic patterns in the same scene. Again, the experiments with adjusting phase relations through window size demonstrate the power of a putative neural mechanism that could make analogous adjustments of phase relations.
Summary
Finding the patterns (basins, sub basins, and general pattern) in the world around us is nontrivial and important. We have shown that adjusting phase relations between a visual representation and the dynamics of a system is a way to extract many different patterns within the system's dynamics. We propose that the apparent motion phenomenon presupposes that neurology has a way of of adjusting phase relations between the dynamics of the retinal image and the final representation as experienced. Since that mechanism is in place, we propose it as a candidate for the extraction of complex patterns from complex systems.
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