This is a very interesting visualization. If you adjust col2, you can see that the illusion basically has a step function. If both line colors are darker than the background, the two patterns look the same. If you slowly adjust col2 until it matches the background and then becomes just a hair lighter, they pop into existence with the full illusion. There is no transition whatsoever except insofar as you can't see the lines when they match the background color.

How are you adjusting the colours? The page is not interactive on my device, and I see no controls of any sort.