"What is a Labyrinth to a Topologist?
"We arrive at the most fascinating application. A labyrinth does not look like a polyhedron, but topology taught us to abstract. What is a labyrinth in its purest essence? It is a graph: a set of nodes (intersections) connected by edges (corridors). This idea of reducing a complex map to a connectivity graph is, in fact, the very origin of topology, used by Euler in 1736 to solve the Königsberg Bridges problem. A labyrinth is, therefore, a topological space that we can analyze.
"The Algorithm as a Topological Explorer
"In our final simulation, we do not have a static labyrinth, but a Genetic Algorithm (GA) trying to solve it. A GA mimics biological evolution: it creates a “population” of hundreds of possible paths (the “individuals”); evaluates how “fit” they are (how close they get to the exit); and the best individuals “reproduce” (their paths are combined) and “mutate” (small random changes).
Generation after generation, the population evolves toward an optimal solution. Crucially, the GA does not explore just one path, but deploys an “exploration network” that covers vast areas of the labyrinth simultaneously. We can measure the shape of that network."
https://sergiogevatschnaider.substack.com/p/the-hidden-shape-of-the-world