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A few ant robots are placed in a labyrinth, formed by a square lattice with a small number of corridors removed. Ants move according to a deterministic algorithm designed to explore all corridors. Each ant remembers the shape of corridors which it has visited. Once two ants meet, they share the information acquired. We evaluate how the time of getting a complete information by an ant depends on the number of ants, and how the length known by an ant depends on time. Numerical results are presented in the form of scaling relations.
There are strong indications that the history of design may have begun with the concept of a meander. This paper explores the application of meanders to new classes of meander and semi-meander knots, meander friezes, labyrinths and mazes. A combinatorial system is introduced to classify meander knots and labyrinths. Mazes are analyzed with the use of graphs. Meanders are also created with the use of simple proto-tiles upon which a series of lines are etched.
In this paper, we introduce a new method for counting the number of connected components of multi-curves. Our method is based on associating multi-curves with permutations, where we can see that the number of connected components of a multi-curve is directly related to the number of cycles in a cycle decomposition of the corresponding permutation. Our ultimate goal is to obtain a formula about multi-curves that gives the number of connected components of the curves, and obtaining a formula for the number of cycles of a permutation will also accomplish this goal. While we have several naive methods for counting the number of cycles of permutations, none of them gives us such a formula. As an approach, we develop a new combinatorial technique to count the number of cycles of permutations by introducing a new notation of permutation.
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LAByrinth - Magnifying science through the lens of design and culture.