Henry Baker wrote:
Can't modern GPU's (nVidia Kepler, etc.) compute Mandelbrot in "real time" -- i.e., the time it takes to display that portion of the screen ? If not, aren't modern GPU's getting pretty close to this capability ?
Yes, real-time rendering on a GPU is pretty trivial these days. I implemented it as a screen-saver a couple years ago, see: http://mrob.com/pub/comp/screensavers/index.html#GLMZ As an added bonus, I was able to use the GPU to interpret hand-gestures on the webcam as a hands-free input technique to zoom in and out. I got 1024x1024x11500 iterations per second on an Radeon HD 6750M. (On my Radeon HD 5770 it's about 1.8x faster). This is more than adequate for most users, even without smart techniques (as used by XaoS, [5]) to avoid re-computing pixels, etc. But on a GPU, to zoom in to the really interesting stuff, you need "fast double precision" that is unlocked, as in the hyper-expensive Nvidia Tesla cards, or something like the Radeon 6900 or 7900 series. And for the really *really* interesting stuff, as seen at [6] (scroll down), you need much better than double precision. Adam P. Goucher wrote:
As a computational tour-de-force, I decided to draw a large image of the Mandelbrot set and save it as a macrocell file. The iteration limit was 1000 iterations per pixel, and the bounding box is 258687 by 221688. [...]
The biggest Mandelbrot images that have been *computed* (as far as I know) are 2097152 x 2097152 in size. They were done by Thorsten Förstemann on his dual Radeon HD 5970 system, as described at [1]. Each 5970 has two GPU chips, each with 1600 shader cores, for a total of 6400 cores (see [2]). It took him 3028136 seconds (about 35 days) to do the calculation 20 times using almost identical but slightly different grids. They were iterated to a maximum of 8589934592 (2^33) iterations. However, he did not store the results (the purpose was to measure the area of the Mandelbrot set, so only a count of pixels was needed.) The Radeon 5970 is pretty old now, see [3] to put its stats in perspective and [4] for a comparison to Nvidia. - Robert [1] http://www.foerstemann.name/dokuwiki/doku.php/area:start [2] http://www.foerstemann.name/dokuwiki/lib/exe/fetch.php/area:2012-02-22-sysin... [3] http://en.wikipedia.org/wiki/Comparison_of_AMD_graphics_processing_units [4] http://en.wikipedia.org/wiki/Comparison_of_Nvidia_graphics_processing_units [5] http://wmi.math.u-szeged.hu/xaos/doku.php [6] http://mrob.com/pub/muency/secondorderembeddedjuliase.html -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com