“Unless a grain of wheat falls into the earth and dies, it remains alone; but if it dies, it bears much fruit.” – John 12:24
“The last enemy to be destroyed is death...Death is swallowed up in victory.” – 1 Corinthians 15:26, 54
"The greater the sin, the greater the mercy, the deeper the death and the brighter the rebirth.” - C. S. Lewis
"This story...has the very taste of primary truth." - J. R. R. Tolkien

Sunday, June 7, 2009

The Mandlebrot Set

The Mandlebrot Set is the set of complex numbers c such that the series zn+1=zn2+c (where zo=0) is bounded (it does not tend to ∞ or -∞). For some examples and more information, see wikipedia. Since, in the complex plane, the complex number a+bi is plotted at the coordinates (a,b), a set of complex numbers is represented as a region of space in the complex plane. The Mandlebrot Set is the black region shown here; its boundary is a fractal:

Slightly zoomed in:

Here are a couple videos that zoom in on different "places" in the Mandlebrot set:

In the words of physicist Roger Penrose, "The Mandlebrot Set is not an invention of the human mind: it was a discovery. Like Mount Everest, the Mandlebrot set is just there" (Penrose, The Emperor's New Mind). The fact that the Mandlebrot set "is just there" is remarkable. It's mere existence is worth wondering at.

1 comment:

  1. Besides all that, it would be a great name for a band. Maybe an avante garde jazz thing...