Hi Andrew,
I'm sure I've seen mention of such a thing on this Forum within the last 6 months.
I'd be surprised if such a thing didn't exist as RGB is popular.
Have you searched Farnell?
My code was not PICAXE BASIC unfortunately.
Basically, I had a DO loop of length 100 so that RGB values were in percents.
Then load the separate RGB values into 3 variables.
Run the loop. Decrement the variables on each loop.
Have a conditional to test variable >0. If so have an output. If not deassert.
This is like a home-made PWM.
I didn't use the PIC PWM as it was a dedicated chip.
My own code added multiplexing and ADCing (overheat thermistor) and reading the USART buffer.
This allowed the PIC (18F25K20) to control 8x RGB+W channels.
4 'PWM' channels plus 8 lines for MOSFET control.
And serial control like an LCD firmware chip. (Address,%R,%G,%B,%W)
And reducing power in overheat condition and reporting back to Host.
I'm sure with a fast x-Y decoder you could multiplex even more.
The bit I was pleased about most was my serial read+process without flicker.
I interleaved the processing so that it was 'hidden' time-wise amonst the muliplexing. No gaps, no flicker.... feeling good...
I think each individual RGBW ran at about 3kHz , so fairly stable. But you could see the strobe effect if you really waggled your eyes. (Far less flickery than most car rear red sidelights!!).
I don't even know where it is now. I only did it as an exercise.
To try and do the same thing with an X2 PICAXE may be possible but I think you could only do one if you wanted it fairly flicker-free.