Monthly Archives: April 2021

The Mandelbrot generator has been added to the Imaging Whiteboard. The whole point of the Mandelbrot is infinite complexity from a simple algorithm. The plot points are generated with only 5 lines of code:

                    Complex z = new Complex(0.0, 0.0);
                    Complex c = new Complex(((double)w - MandelbrotSize / 2 + 
                                             HOffsetSliderValue) / (ZoomSliderValue * 64), 
                                            ((double)h - MandelbrotSize / 2 + 
                                             VOffsetSliderValue) / (ZoomSliderValue * 64));
                    uint iteration = 0;
                    for (; iteration < maxIterations && z.Magnitude < 2; iteration++)
                        z = (z * z) + c;

The control allows the user to zoom into details of the Mandelbrot and generate details.

The detail shown above is from the very left tip of the full scan. It seems that this detail repeats the full scan, but, not exactly. At first glance the Mandelbrot seems to contain much repetition; unlike fractals these repetitions are not exact.

The full un-zoomed plot looks like: