ΔE 11.2, fair: the same colour family, but not a straight swap. Blue Ink is a little lighter, cooler than Cultist Purple. They are different kinds of paint: Army Painter Cultist Purple is an opaque base/layer paint and Formula P3 Blue Ink is an ink, glaze or transparent paint, so they won’t behave the same on the model even where the colour is close.
Only where an exact match doesn’t matter, such as a new unit or a highlight. Fair match (ΔE 11). Blue Ink is a little lighter, cooler than Cultist Purple. They are different kinds of paint.
The same difference applies the other way round: Cultist Purple is a little darker, warmer.
ΔE is the colour difference between our two swatch estimates: under about 6 is close, over about 15 is loose. Real paints also differ in finish, coverage and how they thin, so test before you commit.
See Cultist Purple on the colour wheel See Blue Ink on the colour wheel
All matches: Cultist Purple equivalents · Blue Ink equivalents