I am looking at fading code,

I am looking at fading code, and see code examples to fade entire strips/rings from one color to the next. How would code be written to fade a single pixel to the next, such as a single pixel fades out (white to black) while the next pixel in the chain fades in (black to white)? This would give the basic illusion that the white pixel has slowly moved its position in the chaIn.

Have you looked at the blend function? You can fade out by blending toward black, and fade in by blending toward your target color.