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The fluctuation of the slip is proportional to the patch radius (Sekiguchi et al. 2008).

"Patch radius" represents the two-dimensional distance within the model space between agents.

Global environmental conditions for time and distance from other agents are defined using the NETLOGO standard protocols of "ticks" and "patch radius.

Distance is measured based on the NETLOGO model protocol with a starting patch radius of one agent-worker per ten model patches.

The RCPA, introduced by the authors in [18], consists of a circular patch radius of which can be electrically varied by turning all the switches on and off simultaneously.

As shown in Fig. 1A, we set a single patch in the model domain and employ the model parameters summarized in Tables 1 and 2. We then vary the patch radius and the scaling relation of (w_{c}) in Eq. (4). Figure 1B illustrates the frictional relationship, assuming (w_{c}) scales with respect to (R).

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The nucleation size is proportional to L. Since the brittleness is assumed to be the same for Patches L and S, the values of L inside those patches are proportional to the patch radii.

Comparison stimuli (Fig. 2) consisted of uniform circular patches (radius 32 pixels, 0.33, 0.67 or 1.33 deg) whose luminance was varied (4 levels, chosen so that the lowest luminance resulted in ca. 10% brighter-than judgments and the highest ca. 90%.

In order to investigate an elementary process in the hierarchical asperity concept, which is the interaction of two length scales different by one order in the hierarchical structure, one Patch L (radius R L, nucleation radius R L c ) having one Patch S (radius R S, nucleation radius R S c ) was considered and embedded in a rate-strengthening fault.

Figure 2a and b provides a snapshot of a single patch with radius (R = 20;{text{km}}), (w_{0} = 0), and (gamma = 2).

The simulations were conducted until 20 large earthquakes occurred, which were approximately Mw 6 for the Patch L radius R L  = 4 km.

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