Think Agate, think stripes. Agate is one of the most colourful and varied of stones coming in an enormous range of colours and textures. It is actually a Chalcedony Quartz, very fine grained, that forms slowly within cavities in volcanic and some metamorphic rocks. The stripey banding is analogous to the growth of tree rings. Agate is often found eroded out in rivers as nodules or geodes (often with quartz and amethyst centres, or in some cases opal).
The exception to the stripey rule are varieties like Moss Agate and Blue Lace Agate. These are a sub group called dendritic agates that have fern like patterns caused by inclusions of metallic compounds.