Physical Maze Solvers. All Twelve Prototypes Implement 1961 Lee Algorithm

Abstract

We overview experimental laboratory prototypes of maze solvers. We speculate that all maze solvers implement Lee algorithm by first developing a gradient of values showing a distance from any site of the maze to the destination site and then tracing a path from a given source site to the destination site. All prototypes approximate a set of many-source-one-destination paths using resistance, chemical and temporal gradients. They trace a path from a given source site to the destination site using electrical current, fluidic, growth of slime mould, Marangoni flow, crawling of epithelial cells, excitation waves in chemical medium, propagating crystallisation patterns. Some of the prototypes visualise the path using a stream of dye, thermal camera or glow discharge; others require a computer to extract the path from time lapse images of the tracing. We discuss the prototypes in terms of speed, costs and durability of the path visualisation.

The Electron in the Maze

“…With this physical method, the maze resolution is fast. This explains why this is considered to be the fastest and the cheapest method among many other physical methods [3], especially if the circuit is drawn by ink pen on a paper sheet.…”

Maze Solvers Demystified and Some Other Thoughts

“…Chemical, physical and living maze solvers are conventional examples of unconventional computers. In the present chapter we do not provide all technical details of the experimental laboratory prototypes, these can be found in [6], but rather share our thoughts on maze solvers in a context of unconventional computing and discuss some experiments with inconclusive results.…”

“…To solve a maze 2 is to find a route from the source site to the destination site. In [6] we reviewed experimental laboratory prototypes of maze solvers. We speculated that the experimental laboratory prototypes of maze solvers, despite looking different, use the same principles in their actions: mapping and tracing.…”

Droplets As Liquid Robots

“…In all articles where it was shown how chemotactic droplets can solve a maze, the droplets have in fact followed the shortest path predefined by a concentration gradient in the channels of the maze. Therefore diffusion and Marangoni flows are the physical solvers of the maze in principle, and the droplet follows the gradients in order to minimize its free energy [2]. The chemoattractant (i.e., the chemical substance placed at the exit) diffuses and causes a surface tension gradient that a droplet can sense.…”

“…As a control, droplets without HDA have not shown chemotactic ability and have not followed the gradient. In principle, the H + ions from the target of the maze were the physical solvers of the maze, while the droplets enabled visualization of the shortest path [2].…”