What this course is about

Nature and technology are full of systems in which large-scale order emerges without central control. Birds flock, fish school, ants coordinate, tissues organize during morphogenesis, and physical systems form ripples, dunes, or snowflakes. Similar principles appear in traffic flow, decentralized power grids, social networks, and swarm robotics.

What these systems have in common is that global behavior emerges from local interactions in settings that are often nonlinear, stochastic, and far from equilibrium. Predicting such behavior is difficult. Even small changes in microscopic rules can produce qualitatively different macroscopic outcomes.

In this course, we study such emergent phenomena computationally. Using simulation, data analysis, and machine learning, we investigate both the forward problem — given a set of rules, what collective behavior emerges? — and the inverse problem — given a desired emergent function, which local rules can produce it?

What students will do

The course combines short student presentations on foundational papers with hands-on computational project work. Participants will work with agent-based and particle-based models, define quantitative measures of collective behavior, and use optimization and machine learning to tune systems toward target behaviors.

• Implement classic models of self-organizing systems, or build on provided starter code.
• Explore how different local interaction rules shape global dynamics.
• Define order parameters and evaluation metrics for collective behavior.
• Study robustness under noise, perturbations, and changing environments.
• Use optimization and ML methods to discover or improve interaction rules.
• Work in small teams on a project challenge and present results in a final demo.

Example project directions

Depending on student interests and background, projects may focus on topics such as:

• Robust flocking and collective navigation
• Collective transport and cooperative task solving
• Self-assembly into target structures
• Decentralized maze solving
• Synchronization and swarm formation
• Self-replication or regeneration-like behavior in model systems
• Learning interaction rules for desired emergent functions

Projects will be developed collaboratively in subgroups of 3–4 students, with room for friendly competition between different approaches.

Methods and tools

We will work primarily in Python and, where useful, optionally in C++, JavaScript or other tools. Depending on the project, students may use or extend computational tools such as:

• Agent-based and particle-based simulations
• Order parameters and collective-behavior metrics
• Black-box optimization and evolutionary strategies
• Differentiable simulation approaches
• Reinforcement-learning-inspired optimization
• Scientific computing and visualization workflows
• Frameworks such as HOOMD-blue and JAX MD

Why this course is interesting

Emergence sits at the intersection of physics, biology, engineering, mathematics, and computer science. Understanding it is scientifically fascinating; learning to design it is even more powerful.

This course is for students who enjoy thinking across disciplines, working with simulations, and turning abstract ideas into computational experiments. It connects fundamental questions about life-like behavior with modern tools from machine learning, optimization, and scientific modeling.

What you should bring

• Experience with Python scripting or scientific coding
• Familiarity with NumPy, plotting, and basic debugging
• Basic background in physics, engineering, mathematics, or a related field
• Interest in machine learning, optimization, or data-driven modeling
• Your own laptop and the ability to set up a local Python environment (Conda or venv)

Prior deep expertise in machine learning is not required, but curiosity and willingness to experiment are essential.

Course format

The course combines introductory lectures and discussions, student presentations of seminal papers, guided computational exercises, and team-based project work culminating in a final presentation or demo. Students will not only learn key concepts of emergent behavior, but also build and test models themselves.

Selected inspirations and resources

• Brainxyz video — Create life from a simple rule
• Complexity Explorables — Explorations of complex systems
• Lenia — Continuous cellular automata and artificial life
• Boids — Interactive flocking demo
• HOOMD-blue — Particle simulation tools
• Vicsek & Zafeiris (2012) — Collective motion
• Mnih et al. (2015) — Human-level control through deep reinforcement learning
• O’Keeffe, Hong & Strogatz (2017) — Oscillators that sync and swarm

Ferienakademie 2026
20 September – 2 October 2026
Sarntal, South Tyrol, Italy