http://www.cygnus-software.com/gallery/1000zooms.htm
1000 Zooms
This particular picture, generated in Fractal eXtreme, is not remarkable for its beauty, but it is quite an amazing picture in another way. This picture just might be one of the most magnified Mandelbrot sets, or indeed one of the most magnified objects of any type, in the world. This picture is zoomed in exactly one thousand times. In other words, the magnification was doubled a total of one thousand times, giving a total magnification of 1.07 times ten to the three hundred and first power. That's a one followed by three hundred and one zeroes. That's serious magnification. To put that magnification in perspective it helps to know that at a magnification of ten to the twenty first power, a typical computer monitor would be about the size of the milky way galaxy. At a magnification of ten to the fortieth power, an electron would be about the size of the visible universe. The magnification of this picture is ten to the three hundredth power. An average of twenty thousand iterations were done for each pixel in this picture. Each of these iterations involves a number of additions and subtractions, but most importantly, three multiplications. Each of these multiplications has to be done to more than three hundred digits of accuracy, which means that the poor program has to do hundreds of smaller multiplications and additions just to do one three hundred digit multiply. Small wonder that even with very efficiently coded math routines and two Pentium® Pro processors, it still took 36 hours of calculations to render this picture. One hundred forty thousand pixels, times twenty thousand iterations per pixel, times eleven hundred and forty multiplications per iteration comes out to 3.2 million million multiplications, each one of two ten digit numbers. Plus about ten million million additions and subtractions. That's a lot of math. Fractal eXtreme has actually been tested at much higher magnification levels than this picture -- all the way out to seven thousand two hundred zooms! However the test pictures we created at that magnification were exceptionally boring, so we're not posting them here. You probably won't ever zoom in this far with Fractal eXtreme. There's a lot of beautiful places to be found at far more modest zoom levels. But it's good to know that if you're hot on the trail of an elusive picture, you never have to worry about Fractal eXtreme running out of accuracy, because it's been torture tested at magnifications that make the entire universe seem small. |
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