But still, the mechanism by which how the amoeba maintains the quality of the approximate solution, that is, the short route length, remains a mystery. It seems that spatially and temporally correlated movements of the branched parts of the amoeba located at distant channels are the key. Each of these branches is oscillating its volume with some temporal ‘memory’ on illuminated experiences. Groups of the branches perform synchronization and desynchronization for sharing information even though they are spatially distant.”

But still, the mechanism by which how the amoeba maintains the quality of the approximate , that is, the short route length, remains a mystery. It seems that spatially and temporally correlated movements of the branched parts of the amoeba located at distant channels are the key. Each of these branches is oscillating its volume with some temporal ‘memory’ on illuminated experiences. Groups of the branches perform synchronization and desynchronization for sharing information even though they are spatially distant.”

2013 I made an approximate solution to the traveling salesman problem using the idea of rubber bands and a methodology with pen and paper.
 
2017 I found confirmation — somebody wrote a paper expressing a similar notion that year.
 
Of course the slime mold (and now the digital slime mold) provides even more confirmation. None of these are solutions but they’re good approximations.
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