We report a series of experiments that employed chromatic variants of lightness illusions in an attempt to gain theoretical leverage into the types of computations that are responsible for the illusions. Two types of displays were used: one that elicits a strong percept of transparency and one that does not. We compared the pattern of induction observed in chromatic and achromatic variants of both display types. We found that the pattern of induction observed in the display that evoked a strong percept of transparency generated similar patterns of induction in both the chromatic and achromatic variants of the display, suggesting that layered image representations (scission) may be responsible for the induction observed in this display. In contradistinction, we found that the chromatic and achromatic variants of the checkerboard-gradient pattern did not consistently generate the same patterns of induction, suggesting that there are patterns of induction that only arise from luminance modulations in some class of displays. The impact of these results on existing models of lightness is discussed. We suggest that the comparison of chromatic and achromatic induction can provide insights into the computations that are responsible for the role of context in modulating perceived lightness and color.