The phenomenon of self-organization has been of special interest to the neural network community throughout the last couple of decades. In this paper, we study a variant of the self-organizing map (SOM) that models the phenomenon of self-organization of the particles forming a string when the string is tightened from one or both of its ends. The proposed variant, called the string tightening self-organizing neural network (STON), can be used to solve certain practical problems, such as computation of shortest homotopic paths, smoothing paths to avoid sharp turns, computation of convex hull, etc. These problems are of considerable interest in computational geometry, robotics path-planning, artificial intelligence (AI) (diagrammatic reasoning), very large scale integration (VLSI) routing, and geographical information systems. Given a set of obstacles and a string with two fixed terminal points in a 2-D space, the STON model continuously tightens the given string until the unique shortest configuration in terms of the Euclidean metric is reached. The STON minimizes the total length of a string on convergence by dynamically creating and selecting feature vectors in a competitive manner. Proof of correctness of this anytime algorithm and experimental results obtained by its deployment have been presented in the paper.