Material Implementation of Hyperincursive Field on Slime Mold Computer

“Elementary Conflictable Cellular Automaton (ECCA)” was introduced by Aono and Gunji as a problematic computational syntax embracing the non‐deterministic/non‐algorithmic property due to its hyperincursivity and nonlocality. Although ECCA’s hyperincursive evolution equation indicates the occurrence of the deadlock/infinite‐loop, we do not consider that this problem declares the fundamental impossibility of implementing ECCA materially. Dubois proposed to call a computing system where uncertainty/contradiction occurs “the hyperincursive field”. In this paper we introduce a material implementation of the hyperincursive field by using plasmodia of the true slime mold Physarum polycephalum. The amoeboid organism is adopted as a computing media of ECCA slime mold computer (ECCA‐SMC) mainly because; it is a parallel non‐distributed system whose locally branched tips (components) can act in parallel with asynchronism and nonlocal correlation. A notable characteristic of ECCA‐SMC is that a cell representing a spatio‐temporal segment of computation is occupied (overlapped) redundantly by multiple spatially adjacent computing operations and by temporally successive computing events. The overlapped time representation may contribute to the progression of discussions on unconventional notions of the time.