Agates mostly occur as nodules in volcanic rocks or waters containing Silica in solution which is possibly derived from the decomposition of Silicates in the lava. The Siliceous matter is deposited in regular layers resulting in the banded or striped formation. It is very unlikely that you would ever find an exact duplicate of any type of Agate, Brazilian or other.
Sagenite, or more accurately, sagenitic agate is any agate having acicular or needle-like mineral growths. These hair like filaments are often arranged in fans or sunbursts. The inclusions come in a wide array of colors.