Study the computational universe of simple programs and their rich behavior. From cellular automata to Turing machines, substitution systems, combinators, hypergraph rewriting and more, simple rules can produce immensely complex behavior. Learn to use computer experiments and ruliological methods to explore the phenomenology and structure of pure computational systems, with potentially broad practical applications and theoretical implications.
This track is soon to be renamed the Ruliology & Pure Computation track. It is ideal for those curious about how simple rules generate complexity, and who enjoy hands-on computer experiments and abstract exploration. Applicants to the Ruliology & Pure Computation track should be familiar with A New Kind of Science. If needed, Week Zero provides an opportunity to strengthen programming skills and prepare for intensive projects exploring simple rules, computational universes and complex behaviors.
Schedule OutlineWeek 0: Before the Summer School
- Students will be provided with self-training tools and exercises in using the Wolfram Language
- Suggested reading: A New Kind of Science and An Elementary Introduction to the Wolfram Language
Week 1: exact dates to be confirmed
- Basics of implementing projects with the Wolfram Language (lectures)
- Personal case studies in innovation (lectures)
- Live innovation and coding sessions
- Mentor pairing and project selection with Stephen Wolfram
Week 2: exact dates to be confirmed
- Hands-on, in-depth training on Wolfram Language technology development
- Lectures and discussions on computational thinking and current strategies
- Guided and solo project time
- Special-topic lectures (previous topics have included science-based careers, how to pick a research project, how to write a paper and how to start a technology company, as well as outlines of physics, aspects of scientific history and much more)
Week 3: exact dates to be confirmed
- Guided and solo project time
- Presentation and Community post preparation
- Final student presentation
- 24th Annual Wolfram Summer School
- Bentley University, Waltham, MA, USA
- June–July, 2026