Twilight Dye, Twilight Hair Dye, Phase Dye, Gel Dye, Pink Gel Dye, Skiphs' Blood, Bloodbath Dye, Fogbound Dye, Shifting Sands Dye, Shifting Pearlsands Dye, Nebula Dye, Vortex Dye, Stardust Dye: All of these dyes use Terraria's default noise texture (at Images/Misc/noise) to create semi-randomness in their effects. Changing this texture would change the randomness, but not the effects.
Prismatic Dye: Images/Extra_156. This texture controls the color of the effect. Note that this texture also controls the Empress of Light's rainbow effects, as well as a few other Empress-related items.