Agate forms in the nodule cavities of volcanic rock when silica-rich fluids seep through the volcanic material. Similar to geodes, layers of chalcedony and quartz are built up within the cavity over time, different minerals and concentrations determining the color of each layer. Crystals can form within the agate, reaching inwards to the center of the nodule.
While they look similar to branching leaves and roots, dendrites are not plants, but a unique crystalline formation common in limestone and rocks that form in it. How do these long, spindly fronds end up in the rocks? It starts with a small crack. Over time, this crack may widen and grow as water seeps through, freezes in the winter, and expands. It's a very gradual process, which lends itself to mineral building. If the water is rich in manganese andd iron, these black and brown minerals may be left behind in these spidery channels.