Figure 7 - uploaded by Kevin German
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In t=1 an additional cross appears. It can be seen how the delayed retraction of the marked space inside the new cross creates a shock wave of unmarkedness outside. After 50 iterations, the CA reaches a stable state satisfying I1.
Source publication
George Spencer-Brown's Laws of Form (LoF) provides important insights and inspiration for all sorts of fields. However, his work often takes place on a purely formal level, although the thoughts are inherently carried by space and form. In this work, we present a set of rules for a cellular automaton (CA) that can be used to simulate LoF in an intu...
Contexts in source publication
Context 1
... the fact that the cells in the CA can only transmit information per tick by their own change of state, the speed of information transmission is finite. This case can be seen in figures 5, 6, 7. In fig. 5 the space is marked with limited speed. In fig. 6, the negation only becomes active with a delay when the markedness reaches the outer cross. In fig. 7, there is even a shockwave/ripple resulting from it, which spreads through outer space. This is due to the fact that the cells surrounded by the new cross change their state only gradually. As already mentioned, the finite transmission speed is compatible with George Spencer-Brown's thoughts [12, p. 59]. However, such ripples do not ...
Context 2
... that can be analyzed in the light of LoF, such as the fact that the border itself must first be differentiated between its interior and exterior sides (here cells) before it can become functional. Or that creating a cross in a marked space initially creates a shockwave of umarkedness due to the finite speed / inertia of the (un)markedness (see fig. 7). Regarding philosophical implications for LoF, it is interesting to see that these dynamics imagined by Spencer-Brown can emerge from local rules (natural laws, so to speak) -with the remark that these rules are more complicated than the laws of form. The significance of this could be addressed in more detail in the future. The ...
Context 3
... the fact that the cells in the CA can only transmit information per tick by their own change of state, the speed of information transmission is finite. This case can be seen in figures 5, 6, 7. In fig. 5 the space is marked with limited speed. In fig. 6, the negation only becomes active with a delay when the markedness reaches the outer cross. In fig. 7, there is even a shockwave/ripple resulting from it, which spreads through outer space. This is due to the fact that the cells surrounded by the new cross change their state only gradually. As already mentioned, the finite transmission speed is compatible with George Spencer-Brown's thoughts [12, p. 59]. However, such ripples do not ...
Context 4
... that can be analyzed in the light of LoF, such as the fact that the border itself must first be differentiated between its interior and exterior sides (here cells) before it can become functional. Or that creating a cross in a marked space initially creates a shockwave of umarkedness due to the finite speed / inertia of the (un)markedness (see fig. 7). Regarding philosophical implications for LoF, it is interesting to see that these dynamics imagined by Spencer-Brown can emerge from local rules (natural laws, so to speak) -with the remark that these rules are more complicated than the laws of form. The significance of this could be addressed in more detail in the future. The ...
