PereGaea

Laslo Godel

3: LISTS

To perceive such objects, the Dynism will need to acquire a few more additions to its Visual Processor that will enable it to convert the Rockpile into stimulus `borders' as well as tones. But before we can see how these new additions work, we must first look at the most fundamental of our own drawing conventions.

 

We use a line of finite thickness to represent the indefinitely thin border separating one stimulus from another, which can be the indefinitely large `stimulus' we describe as `background'. I too am obliged to follow this convention.

Now, if we draw two simple stimuli touching at a common point, this point as you can see resides at the center of a four-arm junction formed by the Borders of the two tonal stimuli with respect to each other, and to their mutual background.

If we then cause one stimulus to overlap the other, the junction turns into an arc Border with two T-shaped Junctions at each end.

 

In these two Tone drawings, the Tones may seem to `smooth' into each other with no borders at all. But this new Dynism's eye must also turn continuous tones into discrete ones - again we'll assume eight - in order to operate. The line drawings show where its eye will place the Borders that result. Even the arbitrarily square borders I've put round both drawings will I hope reinforce the point that all tones must end in a border at some point in space.

In many ways Junctions and Borders could be thought of as the inverse of  Tonal Stimuli in that, instead of extending through visual space, they occupy the minimum possible. We will refer to all such borders and junctions collectively as `Lineals' to distinguish them from Tonal Stimuli, which we'll now call  `Areals'.

To extract its Lineals, the Dynism scans its visual field to extract and match its Input Patterns exactly as before. .

However, its retinal cells must now either become sensitive to borders as well as tones, or split into two, with each alternate cell specializing in one function. The details of how this genetic accident might occur and its precise outcome need not concern us here

But all rules have anomalies. For instance, one might suppose that 9 x 9 cell arrays would be better than 8 x 8 since they would allow vertical or horizontal Lineals to be centered in them. But the same result can be acheived by a modifying rule 3 so that such Lineals must pass through the leftmost pair of the four centre squares or the bottom pair.

As these examples suggest, there is a huge range of possible Junctions and Borders, which would appear to make it necessary for the Dynism to evolve a near-infinite range of Lineal Templates. Also, shallow arcs like Sample 6 or a near-full circle  like that of 8 cannot be matched at all however since they break Rule 3; they fail to pass through the center of the Retinal Array.

The same Lineal may be picked up by several boxes, since the Processor has no way of determining where its `ends' are. For instance, the complex curve of Sample 11 may be represented by one straight line Pattern, two smaller Arc Patterns, plus perhaps a short Straight. Sample 12 might be matched as a Junction by the Box containing it, but its curved arms might also be matched to two Arcs plus a Junction by a Box the next size down.

Firstly, there is a simple way of solving  the` too many' Lineals problem. A mechanism we'll call a `Tester' determines whether or not a Lineal separates just two tones from each other, which can only happen if it detects straights, arcs, angles or more complex Tone-pair Lineals..

Then it attempts to match them against just seven templates that correspond to the following Lineals:

It can do this because the Virtual Box we saw earlier can now succesively rotate each incoming pattern by 22.5 degrees until it can be matched to one of the seven Lineal Templates. A Rotation Flag can then be attached to the matched Pattern.

Multi-arm junctions like these however will be treated quite differently. They are `matched' by Testers solely to see how many arms they have, using the center and outermost cells in a Box respectively. The maximum number of arms they can test for is eight. Rotations need not be extracted or recorded.

All Patterns of whatever type, Lineals or Areals, along with all their flags, are now passed to a special type of random access memory, called an `Object RAM'. This records the positions at which they were extracted from the Dynism's visual field, which at this stage corresponds to all the cells in all the Boxes of its eye.   The position of each Pattern is recorded using its lower left center square.

Each of the tonal stimuli the Dynism responds to, as we saw earlier, is defined by its borders. You could think of its borders as being made up of a sequence of Lineals which proceed around it in a fixed order, or rather the Numbers that represent them. This sequence, via their Locations in the Object RAM, is in effect what `joins' them all together. Here we see a `leaf' from the Rockpile Flower both as a tone stimulus and as a `List' of Lineals.

Each of the Dynism's Tone Templates now also acquires such a Lineal List. When a tonal stimulus cannot be Identified, perhaps because it is shadowed or partly obscured by another, the Processor constructs a Lineal List from its raw Input Pattern, that is, before it is shrunk or stretched or rotated. It then searches the Object RAM for the List with the largest number of Lineals that matches it both in kind and in sequence. Again a minimum of three is required to reduce the risk of a mismatch.

More advanced Dynisms develop Testers that compare Lists from two stimuli with exactly the same tone. If both have lists which can be matched to a complete list for the entire stimulus, this may then allow the Dynism to Identify stimuli - or Objects - that have been visually divided by others.