Using the Apparent Motion Mechanism
to find
Basins and Sub-basins
Representational Mode: Visusal
Tool: Smilie Motion
Instructions for Motion Smilie
The Sound interface is disabled on this Applet

FIRST: 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 or fps) 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 20 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.

(For experiments invovling apparent motion: If the particular experiment you are doing involves apparent motion effects, setting the delay between interations so that the ips is between 20 and 66 ips shoulc let you experience accurate apparent motion effects.)

NOTE: Changing Window Size (if that control is enabled) changes ips (smaller windows paint at a higher speed in ips), so you may have to adjust speed when you change Window Size.

Basin Length = 14. This means that Window Sizes that are interger mulitpls of 14 (i.e., 14, 28, 42, 56, 70, 84, 98, ...) will be static.

Sub-basins of lengths 1, 2, and 7 are also present. This means that Window Sizes that are interger multiples of 2 (e.g., 58, 60, 62), interger multiples of 7 that are not mulitples of 14 (e.g., 7, 21, 35, 49, 63, 77, 91, ...) will freeze certain nodes (horizontal rows) but not others. The frozen nodes will be in a sub-basin whose cycle repeats within the overall basin of the system.

Experiment 1. Set Window Size to a multiple of 14, say 42. Notice that the whole system "apparently" freezes. It hasn't. The dynamics are running just as fast as it always did. Notice the fps rate. The dynamics are being painted actively to the screen as fast as ever. It's Apparent Motion (really it's the converse, Apparent Stability) makes the pattern look static. Think about what this implies abaout the functionality and utility of the neural circuits that produce the "illusion" of apparent motion is our ability to perceive complex dynamic patterns.

Experiment 2. Set the Window Size to some mulitple of 7 (which is not also a multiple of 14), say, 49. Notice that there are nodes whose cycle is 7 long nested within the system whose overall cycle is 14 long. These we call sub-basin. We have now frozen nodes in a sub-basin of lenght 7. They are really not frozen or stopped. They are being painted to screen as fast as ever. It is the relationship between the timing of their painting and your neural circuitry that makes them "apparently" static. Again, think about the implications for our ability to perceive subsets of the dynamic patterns.

Experiment 3. Set the window size to some intermediate value (between multiples of 7), say 53. Notice how you perceive certain clusters of nodes (rows) moving in distinct dynamic patterns. The whole system (all nodes, that is, all rows) is being painted simultaneously on the screen every iteration. So it is an "illusion" of apparent motion neurology that the different rows appear to move differently. But it is an illusion that potentially has a profound utility: It may allows us to "see" different dynamics as moving at different rates and in different directions. It may allow us to visually parse the universe of dynamic pattern.

Epistemological Question. If we construe the input of the universe as a dynamic system, what sort of perceptual mechanisms do we have to perceive both its basin structure and also the smaller cycles that occur within its larger cycles. The fact apparent motion (previously considered to be an illusion) mechanisms can freeze basins and sub-basins suggests that the neural mechanisms that produce apparent motion effects may have a deep function in perceiving dynamic (versus static) patterns.