Javier Burgos-Salcedo, Carolina Sierra

The main doubt that exists about the appearance and subsequent development of life on earth, regardless of whether its origin is due to panspermia or abiogenesis processes, is related to the necessary conditions so that, once implanted or synthesized, life can be established and prosper. Following the idea proposed by Darwin in 1873 that the origin of life took place in "warm shallow pools" located on newly emerged land, a mathematical model of a Darwinian pond system is proposed, taking into consideration that, within the classification of fractional Brownian fractals, Mandelbrot addresses the study of the areas of islands, lakes and ponds, which in the present study will be called pond system, which will be understood as a set made up of a finite hyperbolic structure and connected to shallow hollows filled with warm seawater to the edge, which, upon receiving a small volume of additional water, will drain into other hollows, following a continuous downward path towards the sea. These geometric considerations turn out to be decisive for the establishment and subsequent development of emerging life forms on the archaic earth, whose predator-prey type dynamics are associated with a system of medium-sized ponds. The present study supports the theory that life on Earth first developed in small bodies of saline water located on dry land, and emerged through extensive geological processes 4 billion years ago, from where it subsequently flowed to the sea