The Martyr and the Magician
A white, soft, metallic stone whose component molecules are easily rearranged into a countless number of stable configurations. White materia, or undifferentiated materia, has a standard, neutral crystal lattice.
The moldable nature of materia gives it a special property: the patterns of thought (see Theory of Magick) from individuals in proximity to white materia become imprinted on the materia thus differentiating it. Usually, extreme experiences or emotions become imprinted on nearby white materia. For example, white materia in the stone beneath an epic battlefield might be imprinted with the patterns of thought concerning sword play. This swordplay materia could then be extracted and placed in a sword. The wielder’s unconscious thoughts (being close to the materia) would be naturally guided by the pattern in the materia to grant skills of incredible swordplay (thus explaining +1 or +2 swords).
Differentiated materia (colored materia) essentially acts as a record of thoughts and cosmic knowledge. The patterns imprinted on materia guide the unconscious thoughts of sentient beings in proximity to the stone. The possible effects range from being able to cast a new spell, being a better swordsman, having a passive defensive benefit, and many others.