• Senior Thesis
• Department of Mathematics
• Harvey Mudd College

Stephen Haas

Harvey Mudd College Mathematics 2003

Thesis Proposal:	The Hausdorff Dimension of the Julia Set of Polynomials of the Form z^d+c
Thesis Advisor:	Prof. Lesley Ward
Second Reader:	Prof. Henry Krieger

The Hausdorff Dimension of the Julia Set of Polynomials of the Form z^d+c

In recent years there has been a fair amount of research about the Hausdorff dimension of Julia sets. Among the most interesting is whether the dimension of the Julia set varies continuously with the polynomial generating it. We examine this problem and give a near-complete characterization of the answer for polynomials of the form z^d+c.

Read the final thesis (PDF).

Pictures related to my thesis topic:

• The Mandelbrot Set
• Connectedness Locus of polynomials of the form z^3+c, with marked points
• Connectedness Locus of polynomials of the form z^4+c
• Connectedness Locus of polynomials of the form z^6+c
• Successive zooms on M_3:
  • 1
  • 2
  • 3
• Julia sets for:
  • z^2-1
  • z^2+.5i
  • z^3+i
  • z^4-.83i
  • z^6+.5i
  • z^6+.75i
  • z^6+.77i
  • z^6+.773i
  • z^6+.78i