Optimal Behavior of a Moving Creature in the Cellular Automata Model

Autonomous Roving Object's Coverage of its Universe

“…The task of the creature is to cross all empty cells with a minimum number of steps. M. Halbach and R. Hoffmann found, among other results, that no two-state algorithm allows the creature to cross all cell (the best algorithm covering 61% of cell for a given configuration) [5]. They found also that four-state algorithms provide better results and identified a four-state algorithm able to reach all cells of an empty configuration of size 8x8 [5], see Figure 1 (b).…”

“…M. Halbach and R. Hoffmann found, among other results, that no two-state algorithm allows the creature to cross all cell (the best algorithm covering 61% of cell for a given configuration) [5]. They found also that four-state algorithms provide better results and identified a four-state algorithm able to reach all cells of an empty configuration of size 8x8 [5], see Figure 1 (b). Finally, they were able to identify 6 five-state algorithms able to achieve 100% success, crossing all empty cells, for five reference configurations of the lattice [5], see Figure 1.…”

“…They found also that four-state algorithms provide better results and identified a four-state algorithm able to reach all cells of an empty configuration of size 8x8 [5], see Figure 1 (b). Finally, they were able to identify 6 five-state algorithms able to achieve 100% success, crossing all empty cells, for five reference configurations of the lattice [5], see Figure 1. 3.…”

“…Because simulating such models is extremely computationally intensive, they developed an ad-hoc language [8] and a custom processor [9], both optimized for their research. In [5], [6], and [7] R. Hoffman & collaborators have focused on a simpler problem, a subset of their long term goal. They have investigated a two-dimensional (2-D) cellular automaton (CA) model where a cell can be of type Obstacle, Empty or Creature.…”

“…After 2 million iterations of the program, 28 cells out of 50 free cells were not yet crossed, while R. Hoffman et al reported success with algorithms "57 = ORIL IROL" (see [5], [6], and [7] for results and description of algorithm "57"). The poor result of the random direction selection for configuration (a) was unchanged after 100 million iterations.…”