Representing Dynamics with
Historical Trace
(and with Sound--not currently working)

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Instructions for Historical Trace Representation (Smilie 3)

Historical Trace. You can activate the Historical Trace (Smilie 3) simply by pressing PLAY (though the pattern you see will not be accurate unless you slow down the representation to below 66 frames per second (fps) using the DELAY controls).

System Parameters. This is an N=64, K=3 system where all Nodes are Self-Referencing (that is, they check their own state on each iteration as one of their K=3 inputs).

Epistemological Questions. This particular system has 1000 known basins, that is, (using the TAO Tool) it produced 1000 distinct basins in 1000 perturbations. It certainly has many more. Of those 1000 distinct basins, 206 had a length L=4, 544 had L=8, 102 had L=12, and 124 had L=24. So we can guess that about 20% of the basins have length L=4, 54% have length of L=8, and so on.

How do the two forms of representation (i.e., Twinkling Nodes and Sound on previous applet) or Historical Trace (on this applet), compare for your ability to know this dynamic system? For example, how do they compare in answering questions like those below?

One question is can you distinguish basins of different lengths? That is, when you press the PERTURB button and listen the sounds and/or look at the twinkling nodes can you count the number of iterations before the pattern repeats?

Another question is Can you tell one basin from another? The Twinkling Nodes will have a unique sequence of patterns for each basin. In contrast the sounds are based on sampling from the system [NOTE 2]. So different basins may or may not produce different sounds in this perceptual system. This, of course, is much like the design of the perceptual systems of living beings.

A final question is Can you track all the basins? Because there are so many basins (1000 at least) it is not likely that you will hear repeat basins. So this experiment is not well defined in this case. It would be better to test a case that has fewer, say 10 or 15 or 20, basins.