A Unique Educational & Career Opportunity with Stephen Wolfram

A unique opportunity to do original research at the frontiers of science, the Wolfram Science Summer School teaches about 40 students from a diverse range of scientific backgrounds how to use Stephen Wolfram's A New Kind of Science and the Wolfram Language to implement projects in their fields of interest. Most of these students are advanced undergraduates and early graduate students, but those in different circumstances are considered. We are looking for students who want to enhance their careers with Wolfram Science and the Wolfram Language. Read more »

Class of 2007

Tommaso Bolognesi

Bio [2007]

Tommaso Bolognesi obtained his laurea in physics from Pavia University in Italy in 1976, and his MS in computer science from the University of Illinois in 1982. He is currently senior researcher at ISTI-CNR, an Institute of the Italian National Research Council at Pisa. His initial research interest was the application of stochastic processes and fractals to computer music composition. He then moved to formal specification and verification of concurrent systems, and contributed to the definition of the LOTOS specification language (an ISO standard). He has also worked on timed extensions of process algebra, the relations between graphical and algebraic representations of process networks, specification styles based on constraint composition, their application to various classes of languages, and on the unification of event-based and state-based paradigms. He has been teaching software engineering at the University of Siena for seven years, and is a member of the program committee of several conferences on formal methods. In 2005 he started exploring various aspects of Wolfram's NKS, which is now his full-time research activity.

Project Title

Perturbed Planar Trinet Computations with Two Rewrite Rules


According to an NKS conjecture, trivalent graphs (networks) may represent the appropriate model for our dynamic physical space. We introduce a three-parameter algorithm for growing planar trivalent networks based on the mobile network automaton idea briefly mentioned in the NKS book, and on a complete set of two graph-rewrite rules. The initial trinet is a two-node graph with three parallel edges. We expose complexity by means of a useful revisit indicator that provides a compact visual representation of computations, as an alternative to inspecting huge lists of graphs. The typical features that emerge in cellular automata--periodicity, nesting, deterministic randomness--are also detected by our indicator, and the corresponding trinets exhibit a variety of shapes, including regular or quasi-regular trees, 1D or 2D grids, and graphs with bounded chaotic and unbounded regular components. Furthermore, two most surprising computations are found that yield a remarkably fair and uniform, random-like revisit indicator (presented at the NKS 2007 Conference).

In the context of the Summer School project, after substantially improving the Mathematica 6 code for the above algorithm we have addressed the question: how do different trinet computations react to and/or resist perturbations, such as the loss of a portion of the graph, or a temporary alteration of an algorithm parameter?

Project-related Demonstrations

Planar Trivalent Network Growth Using Two Rewrite Rules

Favorite Outer Totalistic Three-Color Rule

Rule chosen: 13723198

That's rule 13723198. This rule seems to know perfectly what it is doing, and appears somewhat generous in transparently showing the internal steps of its computation. If an analogy were to be found, I would think of the computation performed by a very complicated, but purely mechanical (not electronic) system, with small balls bouncing and dropping and fragmenting in orderly ways.