Representing Dynamics
with
Historical Trace and with Sound
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Instructions
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).
Sound. Sound automatically introduces a pause between iterations to give the sounds enough time to be voiced. Therefore the system runs more slowly, at an appropriate pace for hearing, when you use sound.
You must activate sound by pressing the USE SOUND radio button. It is highly recommended that you also EDIT SOUND by pressing that button. When you do, an interface will appear (see image, below) that allows you customize the sounds you hear as three separate musical instruments. These instruments are controlled by inputs from "sensory" nodes [NOTE 1].
In the image below, the instrument on the far left is set to acoustic base, the middle instrument is set to vibraphone, and for the right-most instrument the menu of 128 instruments is open and kalimba is being selected. The chord check box allows you to set an instrument to play either a chords or a note on voiced iterations. The Pitch Range control allows you to set the three instruments to different octaves so that you can hear them more distinctly from each other. The Volume control allows you to set the relative volumes of the three instruments. The "Play Instrument" button allows you to hear an individual instrument while you are searching one you like. The "Play All" button allows you to play all instruments together to determine if you like they way the sound together and to be sure you can hear each distinctly. When appropriately designed, the three-instrument sound option is a powerful way of comprehending the dynamics of a system and for searching for and detecting basins.
We strongly recommend that you make the instruments as different as possible from each other and in different pitch ranges, so that you can hear the patterns resulting from system dynamics more clearly.
The idea here is not to make music but to use your auditory sensory ability to apprehend the pattern of a dynamic system.
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, Sound and Historical Trace, 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.
NOTE 1. The sound interface is driven by the states of the top row of 15 sensory nodes and will not function if they are not connected. When they are connected, (i.e., when the top row of sensory nodes is taking input from the system), the sounds it outputs depend on the dynamics of the specific nodes that those 15 sensory nodes sample from. Furthermore, how the sensory system interprets the dynamics it samples depends on the logic of the truth tables for those 15 sensory nodes. A final point about sensory nodes is that they can accept input from other sensory nodes so that you can model sensory networks. The sound patterns that you hear are candidates for emergent patterns that result from the dynamic processes (binary nodes in logical relation to each other) of E42.
The top row of 15 sensory nodes (see Node Frame figure, above) are divided into three subsets of five nodes; each of these subsets outputs to one of three instruments (see figure below, right). [Technically, one node from each subset (the first, sixth, and eleventh node in the row of 15 nodes) determine if the each of the three instruments are silent or voiced on a given iteration. The other four nodes (i.e., 16 bits) determine which of sixteen notes (two octaves) the instrument will play, if voiced.] A sense of cadence is enforced by the fact of movement through discrete iterations. The Sound Frame introduces a substantial delay between iterations to allow notes (or chords) to be voiced long enough to be easily heard.
NOTE 2. That is, there are 64 Nodes in the system and only 15 Sensory Nodes sampling from those 64 Nodes. Each Sensory Node has K=3 inputs; one of these is from itself because all nodes are self-referencing, leaving K=(3-1)=2 inputs to each Sensory Node from the system Nodes. That means that the Sensory Nodes are taking input from 30 system Nodes (15 Sensory Nodes times 2 free inputs for each Sensory Node).