But can an an LED do THIS?

Non-technical guy, here. Trying to learn for a project I'm doing... A kids' nightlight.

Need a low-power, surface-mount LED with three color settings and a fourth setting that cycles smoothly through the color spectrum.

I ALSO need to be able to dim and brighten. Can anyone point me in the right direction?

Last point... the nightlight will have up to 5 of them. So if I'm also looking for color consistency, am I asking too much?

https://www.sparkfun.com/products/14357
Here is a product that will help. The LED has 32 brightness levels and the Red/Green/Blue each have 256/256/256 levels.
Watch the video to see other products in this series.

Thanks very much! Great video. Seems like a great resource for building a few prototypes. Is there a comparable component that would be more affordable when producing by the 100's? Perhaps looking into the APA102C itself?

Thank you, ronsimpson.

In the second video you can see the little computer that programs the colors. In this case the LEDs are on a rope.
There are competing parts that are almost the same.