Chaos

 Chaos theory, a branch of mathematics, describes complex systems where even the smallest changes can create significant impacts. This concept applies notably to moving bodies, where both the motion and external forces - the four fundamental ones being gravity, electromagnetic, and the weak and strong nuclear forces - can influence the outcome.

This dynamic interaction generates patterns called "attractors," which usually take on a fractal form. Fractals are intricate, infinitely complex shapes that follow specific rules or laws. A classic example is Koch's snowflake, which continually adds triangles according to a 3x law, creating a fascinating and intricate pattern.

While linear equations governed by the order of operations (brackets, division/multiplication, addition/subtraction) rarely create chaos, non-linear equations, in contrast, often give rise to chaotic systems. The field of chaos theory is broad, presenting a multitude of unique problems and conjectures.

Edward Lorenz is renowned for discovering the butterfly effect through his early computer models. This phenomenon theorizes that a seemingly insignificant event, such as a butterfly flapping its wings in the Amazon, could potentially trigger a tornado in Texas. Although this theory remains unproven, it has considerably influenced our understanding of dynamic systems.

Lastly, the three-body problem perfectly exemplifies the complexity within chaos theory. Predicting the gravitational interactions among a star and two planets, or any three celestial bodies for that matter, becomes immensely complicated due to the intricate attractors these interactions form.

 To conclude, chaos is a complex mathematics branch whose laws must be described by a new branch of calculus. A creator of such a branch should win the noble prize and physics and also the fields medal ( an award in mathematics for mathematicians below 40) if this mathematician is under 40.