Divergence from the Mandelbrot Set

Consider the mapping . The Mandelbrot set consists of those complex numbers such that the iterates of do not tend to infinity as . Points with an iterate greater than 2 in absolute value diverge.
In the left-hand image, the norms of red points reach 2 in the fewest number of iterations, followed by the other colors in order of wavelength. The initial image only takes "step size" number of iterations. Check "run" to let the number of iterations increase.
In the right-hand image, white points have iterates with norms less than 2. These are the remaining candidates for membership in the Mandelbrot set.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The default center is in the sea horse valley.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.