We consider an algebraic structure arising from recombination of cellular automata. Cellular automata are discrete dynamical systems with local state \(\mathbb {Z}_{n}\) , and a particular cellular automaton is characterized by a finite sequence of elements in \(\mathbb {Z}_{n}\) . This sequence determines the time evolution rule and it is seen as the genotype of the cellular automata. In Ramos and Riera (Evolutionary dynamics and the generation of cellular automata, 2009) it was defined by a binary operation which determines the recombination of two finite sequences, each associated with a cellular automata. This operation is parametrized by real number, \(\alpha \) , in the unit interval. Therefore, there is a one parameter family of algebraic structures defined on the space of cellular automata. This algebraic structure is noncommutative and nonassociative. The main objective of our work is to study the algebraic structure generated by a finite initial population of cellular automata through recombination. Moreover, we introduce the Cayley graph for the structure, which can be seen as the phylogenetic tree for the initial population. We discuss the structure dependence of the parameter \(\alpha \) , given a finite set of generators.