Iconic operators operate on generalized icons, and change either the logical part (the meaning) or the physical part (the image) of an icon, or both. The concept of duality is essential: iconic operators operate on the dual representations of icons. In other words, the iconic operator operates simultaneously on logical and physical parts of an icon. An essential characteristic of the icon is that the logical part and the physical part are mutually dependent. Therefore, as the image of an icon is changed, so will be its meaning, and vice versa.

An iconic operator OP has two parts: OPm for the logical operator, and OPi for the physical operator. We write:

OP = (OPm, OPi)