page_title: Complex quadratic polynomial
section_title: 2D Parameter plane
hierarchical_section_title: Complex quadratic polynomial / Spaces, planes / 4D space / 2D Parameter plane
caption_attribution_description: English: Uniformization of the interior of Mandelbrot set components using multiplier map: internal rays , internal coordinate
context_page_description: A complex quadratic polynomial is a quadratic polynomial whose coefficients and variable are complex numbers.
context_section_description: The phase space of a quadratic map is called its parameter plane. Here:
   is constant and  is variable.
  There is no dynamics here. It is only a set of parameter values. There are no orbits on the parameter plane.
  The parameter plane consists of:
  The Mandelbrot set
  The bifurcation locus = boundary of Mandelbrot set with
  root points
  Bounded hyperbolic components of the Mandelbrot set = interior of Mandelbrot set with internal rays
  exterior of Mandelbrot set with
  external rays
  equipotential lines
  There are many different subtypes of the parameter plane.
  See also :
  Boettcher map which maps exterior of mandelbrot set to the exterior of unit disc
  multiplier map which maps interior of hyperbolic component of Mandelbrot set to the interior of unit disc
caption: Multiplier map
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