From the Complex Plane to the Infinitely Beautiful

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.

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

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