Functional visualization of Langton’s self-reproducing loop and its soundness against state permutation

It is known that the sectors in cellular automata that exhibit complex behavior accompany a power law in their power spectra. By applying this expertise to extract the sectors where self-reproduction is actively occurring, we have succeeded in performing functional visualization of Langton’s loop. Next, we have investigated the soundness of the functional visualization against the state permutation. We have identified a pair of permutations that might bring about the most different images. As a comparison result, we found that roughly up to 15% of the sectors were classified into different types of power spectrum except for the first three terms.