The same pattern re-appears
I find Mandelbrot set very interesting, that is why I have decided to show it to you from the perspective of physicist. Mandelbrot set is named after Benoit Mandelbrot and it is a fractal. Mandelbrot set is the set obtained from the quadratic recurrence equation:
with Zn = C, where points C in the complex pane for which the orbit of Zn does not tend to infinity are in the set. Treating the real and imaginary parts of each number as image coordinates, pixels are coloured according to how rapidly the sequence diverges, if at all. Not only do colours enhance the image aesthetically, they help to highlight parts of the Mandelbrot set that are too small to show up in the graph. Zooming into the fractal give us really nice results, giving an impression of the infinite richness of different geometrical structures and self similarities. See the real time zooming of the Mandelbrot set in video below. Zooming in the video is repeated four times at different starting points and at the end we show several results of the zooming into the fractal. Interesting fact: as we zoom in deeply, we can see parts of the Mandelbrot that no one has seen before! It is amazing that the simple iterated equation can produce such beautiful works of mathematical art.
It is a sad fact that Mandelbrot set requires a great deal of computation that will be carried out on your computer. The next step is to estimate the potential parallelism of the Mandelbrot set code using environment Tareador and finally parallelizing the code using a parallel programming model OmpSs, both developed by Barcelona Supercomputing Center.