The aim of this study is to propose a method for constructing a conductive paths topology in a 2D area-to-point and points-to-points problem. We focus here on heat conduction, with the goal of decreasing the temperature differences across a domain. We propose a method using a Cellular Automaton (CA) to reshape an initial topology by a thermal gradients attraction-repulsion mechanism. The potentiality of the generated conductive trees is proved through the temperature reductions obtained. We also propose a second law analysis of the problem. This algorithm leads to heat drains that tend to equally sustain irreversibility across the domain.
Keywords: cellular automaton, topology optimisation, heat conduction, tree networks, constructal theory, entropy maps, heat transfer, conductive paths, cooling, temperature differences, temperature reductions, heat drains, irreversibility