Amoeba changes its state constantly for it to exhibit locomotion and hence move around.It has small finger like pseudopodia (meaning false feet) all around its body and when they move , the amoeba's shape changes.Actually , they're the pseudopodia moving constantly which makes it appear that amoeba changes its shape.

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The changing shape and the ability to form pseudopodia in every direction enables amoeba to move in all directions and engulf food from all the directions.