OK let me get this straight.
When S1 is on the blue LEDs are always on. When S1 is off, the blue LEDs are always off.
When S2 is on the purple LEDs are always on. When S2 is off the purple LEDs are always off.
When S3 is on, the purple LEDs are on unless S1 is off or S2 is on.
When S3 is off, the blue LEDs are off unless S2 is on.
Purple fades in when both S1 and S2 are on. If blue was on, it fades out.
If S3 is on, then purple fades out and blue fades on (unless S1 and S2 are on).
When S1 is on the blue LEDs are always on. When S1 is off, the blue LEDs are always off.
When S2 is on the purple LEDs are always on. When S2 is off the purple LEDs are always off.
When S3 is on, the purple LEDs are on unless S1 is off or S2 is on.
When S3 is off, the blue LEDs are off unless S2 is on.
Purple fades in when both S1 and S2 are on. If blue was on, it fades out.
If S3 is on, then purple fades out and blue fades on (unless S1 and S2 are on).