Agate is a cryptocrystalline variety of silica, chiefly chalcedony, characterized by its fineness of grain and brightness of color. Although agates may be found in various kinds of rock, they are classically associated with volcanic rocks and can be common in certain metamorphic rocks.
Malachite is a copper carbonate hydroxide mineral. Malachite often results from weathering of copper ores and is often found together with azurite, goethite, and calcite. Except for its vibrant green color, the properties of malachite are similar to those of azurite and aggregates of the two minerals occur frequently.