The emergent properties of the universe are traditionally attributed to special values of fundamental constants. It has been pointed out that the most obvious empirical fact about our observable universe is its temporal asymmetry: the early universe seems to have been very different in nature from the current one, and may well turn out to have been very different from the future universe too. The universe in its present state is lumpy with structures such as stars and galaxies, black holes and life, at least according to our best models based on the available observable data. But while the presumed early state and the projected late universe are similar in that they are both characterized by minimal entropy, this is so for different reasons. More importantly, structures prevail and entropic histories allow order hitherto only explained by anthropic principles. This project proposes to produce simulations to analyze the initial conditions and entropic evolutions of computational universes. It will do this by using cutting-edge mathematical tools from information theory and algorithmic complexity to study the interplay of complexity metrics accounting for the kinds of structures found in our universe, including life and intelligence. To this end I will monitor the dynamics of these quantities with respect to their dependence on initial conditions and as regards the manner in which they determine the topology of the universe. I will test whether habitable zones of increasing entropy and free algorithmic complexity where structures like life may exist in candidate universes are common and robust or rare and fragile. The approach will tackle a foundational question in modern physics related to cosmology and complexity theory (and other areas such as network biology where causal networks of interacting units are fundamental) concerning the specificity of our universe and the initial conditions that were needed to give rise to and sustain structure, life and intelligence.