Generating a running blob can be achieved by delayed self-inhibition, which drives the blob away from its current location; the blob generates new self-inhibition at the new location. This mechanism produces a continuously moving blob (see Figure 3). The driving force and the recollection time as to where the blob has been can be independently controlled by their respective time constants. The corresponding equations are (cf. Equations 1 and 2):
The self-inhibition is realized by a leaky integrator with decay constant . The decay constant has two different values depending on whether is positive or negative. This accounts for the two different functions of the self-inhibition. The first function is to drive the blob forward. In this case and a high decay constant is appropriate. The second function is to indicate where the blob has recently been, i.e., to serve as a memory and to repel the blob from regions recently visited. In this case and a low decay constant is appropriate. For small layers, should be larger than for large ones, because the blob visits each location more frequently. The speed of the blob is controlled by and the coupling parameter . They may also change the shape of the blob. Small values such as those used in our simulations allow the blob to keep its equilibrium shape and drive it slowly; large values produce a fast-moving blob distorted to a kidney-shape.
Figure 3: (click on the image to view a larger version) A sequence of layer states as simulated with Equations 11 and 12. The activity blob shown in the middle row has a size of approximately six active nodes and moves continuously over the whole layer. Its course is shown in the upper diagram. The delayed self-inhibition , shown in the bottom row, follows the running blob and drives it forward. One can see the self-inhibitory tail that repels the blob from regions just visited. Sometimes the blob runs into a trap (cf. column three) and has no way to escape from the self-inhibition. It then disappears and reappears again somewhere else on the layer. (The temporal increment between two successive frames is 20 time units.)