A simple system

- predictable - regular motion

$$\frac{d^2\theta}{dt^2}=-\frac{g}{l}\sin(\theta)$$

The game of life

the game of life

topic appertizers

The kicked rotator

\[\begin{align} p _{n+1} &= p _n+K\sin(x_n) \mod 2\pi\newline x _{n+1} &= x _n +p _n+K\sin(x_n) \mod 2\pi \end{align}\]

**Complexity Explorable:** [Kick it like Chirikov](http://www.complexity-explorables.org/slides/kickedrotator/)

Self-Similarity

**Complexity Explorable:** [Hokus Fractus](http://www.complexity-explorables.org/slides/fractals/)

Self-Similarity

**Complexity Explorable:** [Weeds & Trees](http://www.complexity-explorables.org/slides/weeds-trees/)

Synchronization

Synchronization

Pattern Formation

**Complexity Explorable:** [Keith Haring's Mexican Hat](http://www.complexity-explorables.org/slides/stripes/)

Pattern Formation

\[\begin{align*} U+2V\rightarrow 3V\\ V\xrightarrow{k} P \end{align*}\]

**Complexity Explorable:** ["Hopfed Turingles"](http://www.complexity-explorables.org/slides/grayscott/)

Critical Phenomena

**Complexity Explorable:** [Barista's Secret](http://www.complexity-explorables.org/slides/percolation/)

Critical Phenomena

**Complexity Explorable:** [Berlin 8am](http://www.complexity-explorables.org/slides/traffic/)

Growth Processes

**Complexity Explorable:** [Microbial growth patterns](http://www.complexity-explorables.org/slides/scotts-world/)

Collective Behavior