From the Complex Plane to the Infinitely Beautiful

The main mathematical news

2012: Lindsey and Thurston discover that any simple closed curve in the complex plane can be approximated by using Julia sets of polynomials.

1977: Mandelbrot relies on computer graphics to visually illustrate Julia sets, and contributes to Fractal theory and Chaos theory.

1918: Gaston Julia analyzed properties of sets of complex numbers which comprise the boundary for a domain in the complex plane. These sets are named after him.

To the MNS presentation

Additional Theorems / conjectures / Open questions

De-Moivre’s formula
Shapes of Julia sets for general polynomial functions

To the MNS presentation

The main mathematical concepts / Principles

Number theory (MSC2010#97F99)

Complex numbers
Polar coordinates
Julia set

Analysis (MSC2010#97I99)

Iterated function
Bounded/Unbounded sequence
Complex functions
Polynomial function
Connected domain
Fractal Theory

To the MNS presentation

To start the presentation click anywhere in the 1st slide.
To move to the next slide use the keyboard arrows