Sets are the fundamental mathematical object. This means that the entirety of mathematics as we uderstand them can be built using the simple notion of sets. This is not to say that formal set theory is a simple area of study. In a very intuitive level, though we can simply regard sets as just collections of objects. Even this definition of sets is strong enough to construct most of the mathematics we take for granted.

# Chaos & Fractals

## The Concepts

### Sets

### Maps

The concept of a map lies in the core of modern mathematics. The term map is synonymous to a function but the word map encapsulates the core idea of a function, that is that a given input is transformed, i.e. mapped, to a specific output.

### Fractals

In mathematics, we describe fractals as those objects that display self-similar patterns. This doesn't require that the same structure remains unchanged at every scale but that alike structures appear. Some important examples are the Kock Snowflake, the Sierpinski carpet or the **Mandelbrot Set**.

## The Team

### Aris

**Description:** Brought up in the slums of Athens, he can be easily spotted because of his long hair and long beard. He's often seen with sunglasses indoors.

**Last day quote:** "That rug really tied the room together."

### Nickolay

**Description:** He came straight from Siberia so he thinks that London's weather is flip-flop weather.

**Last day quote:** "Lads, how do I get matches on Tinder?"

### Rafael

**Description:** Currently going through a identity crisis, he says he's Brazilian and also half Spanish but he went to a French school in the United States.

**Last day quote:** "Robbie you're making me *very* angry!"

### Ramon

**Description:** Always claiming to be taller than he actually is, this short Spanish guy splits his time between Metric and Ethos' swimming pool.

**Last day quote:** "Damn it Aris, what is this 'first book' you keep referencing?"

### Robert

**Description:** Definitely the best French Hornist in the team, he cannot go to the toilet without his MacBook.

**Last day quote:** When asked for a quote he replied: "Can I say something about JavaScript being s**t?"

## Our Approach

### Computational

Exploration

Qualitative research underpins the success of many discoveries. In fact, some solutions cannot be attained analytically at all, giving rise to the use of numerical methods.

### Analytical

Exploration

Proof and rigorous analysis form the foundation of modern Mathematics. It forms the backbone of the tried and tested combination of derived results and supporting qualitative data.

### Mathematical

Extension

Ultimately curiosity is what drives us to extend the horizon of our knowledge. Research off of the beaten path is the most rewarding and exciting and can pave the way for future explorers.