def METHOD_NAME(rarity_sets):
    untameable_regions = [r for regions in rarity_sets for r in regions if r.untameable]
    if untameable_regions:
        svg_output = '\n<g fill="url(#pattern-untameable)" opacity="0.3">'
        for region in untameable_regions:
            svg_output += f'\n<rect x="{region.x}" y="{region.y}" width="{region.w}" height="{region.h}"/>'
        svg_output += '\n</g>'
        return svg_output
    return ''