# Complexity Explorer Santa Few Institute

## Computation in Complex Systems (Spring 2022)

This course is no longer in session.

• Course Introduction
• Two Kinds of Paths
• Polynomials vs. Exponentials
• Divide and Conquer
• Big O and All that
• When the details don't matter
• Exam
• Divide and Conquer Redux
• Dynamic Programming
• Greedy Algorithms
• Reductions and Translations
• Lessons So Far
• The Best of All Possible Algorithms
• Complexity Wrap-Up
• Exam
• Finding versus Checking
• Circuits and Formulas
• More NP-complete Problems
• P versus NP Problem
• Existence and Nonexistence
• Above and Beyond
• Exam
• Real World Problems
• Phase Transitions
• Random Problems
• Solvability Threshold
• Modeling Differential Equations
• Landscapes, Clustering, Freezing, and Hardness
• Exam
• Building Blocks: Recursive Functions
• Building Blocks: Partial Recursive Functions
• λ Calculus
• Turing Machines
• The Halting Problem
• The Grand Unified Theory of Computation
• The Analytical Engine
• Cellular Automata
• Tile-Based Computation
• Dynamical Systems
• Exam
• More from Cris Moore
• Other ComplexityExplorer resources

## The XY Model: demonstration

This demonstration shows a model similar to the Ising Model in which each vertex in the lattice can occupy a range of states (vectors). Nearest-neighbor energy comparisons allow global patterning in the lattice, i.e. neighboring vectors want to coordinate their alignment. Start the demonstration and watch the transition to an ordered lattice. Restart the demonstration a few times. What are the characteristics of the meta-stable configurations that persist the longest? Does the stable pattern look the same? Does the stable patterns emerge after (roughly) the same amount of time?

NOTE: "discrete" shows linear vectors; "continuous" shows vertices color-coded according to the underlying vector.