Your rock appears to be a sandstone cobble displaying iron oxide banding. The banding is the result of redox reactions of iron and oxygen from water passed through the rock. A oversimplified view would be that the iron oxide staining advanced inward from the outer edge of the rock until the water source was removed. The result is the pattern left in the rock. Similar to salt staining that forms on baseball caps caused by sweat that seeps into the hat and then evaporates.