The work draws some fundamental connections between Feigenbaum's golden mean renormalization group and scenario for turbulence on the one side and high energy particle physics on the other side. The analysis which is based on the natural and obvious connections between the Fibonacci-like geometrical growth rate of epsilon((infinity)) spacetime and Feigenbaum's renormalization gives vital information to basic questions not only of quantum geometry, but also of quantum field theory. (c) 2006 Elsevier Ltd. All rights reserved.