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
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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
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