High Resolution Mandelbrot Set
Image with high resolution cannot be generated directly because big image require arrays to be stored in the memory. Consider simple Mandelbrot fractal, escape iterations are calculated on all the points on the plane then image is prepared. On complex plane, calculation of one point is not dependent on the other point. So find escape iteration and write to image. BMP file is suitable to generate fractal images using this way. BMP file has two parts header and bitmap data. First write BMP header which contain all the information of BMP file including resolution, width, height etc. Then start calculations on complex plane, find escape iteration and write it as pixel in BMP file. Same step is repeated on all the points on the plane. Gradually BMP image grows on disk without taking space in memory. Link to Matlab code that was used to generate big images. One disadvantage is that continuous disk access makes the process slow.The biggest image that was generated using this MATLAB code was 35000x35000 large. The BMP image generated was 4GB in size, then using image editor it was converted to PNG image about 30MB in size. Link to this big Mandelbrot fractal image.