A gaming system displays one of a plurality of symbols in each of a plurality of symbol positions, at least one of the plurality of symbols being a target symbol for establishing a direction of shifting and at least one of the plurality of symbols being a magnetic symbol for shifting toward a target symbol. If any generated magnetic symbol is associated with a generated target symbol, the gaming system shifts that magnetic symbol toward the associated target symbol, resulting in an empty symbol position. The gaming system fills the empty symbol position by shifting a displayed symbol or by generating one of the plurality symbols and repeats until no magnetic symbol is associated with a target symbol. The gaming system provides an award for any displayed winning symbol combination. The gaming system removes symbols from each winning combination, fills the empty symbol positions, and repeats as above.