Cool Staining Pattern!

Based on the visual characteristics of the rock shown in the image, here are some possibilities for its identification:

Jasper: Jasper is an opaque variety of chalcedony, which is a type of quartz. It often comes in red, yellow, brown, or green and can have banding or patterns. Your rock's coloration with the reddish-brown and white could fit this description, especially if it has a waxy feel when touched.

Banded Iron Formation (BIF): If the rock has layers of different colors, especially iron-rich layers (red, brown) alternating with silica-rich layers (white, light grey), it could be a piece of a banded iron formation. These are typically found in ancient geological settings and are indicative of early Earth's oxygenation events.

Agate: Agate is another type of chalcedony, known for its fine grain and bright, attractive colors, often with bands or layers. If your rock has any subtle banding or more defined layers, it might be classified as agate.

Iron-stained Quartzite: If the rock has been subjected to metamorphism and contains iron, it could be quartzite with iron staining. Quartzite is metamorphosed.