The example Draw a vortex fractal in C# explains how to draw a vortex fractal.

The example Draw a Mandelbrot set with smoothly shaded colors in C# explains how to use smooth shading when drawing a Mandelbrot set.

This example combines the equations of the first with the color scheme of the second. See those examples and the code for the details.

The shading isn't perfect because the program uses a smoothing algorithm designed for the Mandelbrot set rather than this fractal, but the result is still very nice, particularly for the second smoothing method.