I have introduced native measures of universal complexity i.e. independent of description language and selected feature(s). This was by way of algorithmic probability based on a generalization of a universal n-dimensional Turing machine rather than the a unidimensional tape. I have shown powerful properties of the measure, correlated to intuitive and formal symmetries, and other algebraic and even physical properties. My approach is a solution to the challenge of graph complexity previously identified by Gell-mann and Feldman as an open problem. See papers: J19, J29, J44. Collaborators: Fernando Soler-Toscano, Santiago Hernández, Antonio Rueda-Toicen, Narsis A. Kiani, Kamaludin Dingle, and Ard Louis.
