xMandelbrot on a faster CPU

kw: algorithms, beauty, mathematics

I noted in Mandel Spider my discovery of the xMandelbrot Viewer. It zooms to any level and uses bignum (increased precision) calculations when the zoom level would overwhelm ordinary floating point calculations. I dug into a similar region using the new quad-core CPU computer my son and I recently built. The image below is a deep enough zoom that 38-digit calculations were used, with the limits shown in the Overview pane shown at the bottom of the post. Note that the application needs Java 5 or later, but I found that simple to install.


You find out the extent of calculations by a histogram in the Palette Editor, which was used to set the color palette here. The MaxIterations parameter was set to 500, and the histogram shows that the actual number of iterations ranged from about 300 to about 450.

Such an image requires 15 minutes to produce on the dual-core CPU on my laptop. This took about one minute on the new computer. About a 4x increase is due to the faster processors and that there were four rather than two. The other nearly 4x is due to the faster front-side bus and memory speed.

As you can see in this control panel overview, the X and Y limits only differ after 25 digits. This is a 10-trillion-trillion-X zoom (10 septillion X). There is no real value in such extreme zooms, because the view looks the same after a few thousand X; that is the way fractals are. It simply provides a way to test the efficiency of one's algorithms and hardware.

The main lesson from this is, for more speed, throw more iron at the problem. That is why the weather bureau and military simulation experts keep rushing to produce ever-faster supercomputers. The fastest now are in the petaflop range, approaching an exaflop (10¹⁸ math operations per second). My "poor little" home computer just loafs along at about a gigaflop, a billion times slower, but that's ten times as fast as the early Cray supercomputers. Nice to have a pocket supercomputer when you need it.