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How is this sprite animation / simulation achieved?

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Those are not sprites. You're looking at vector graphics. Each "noodle" is actually a 2D polygonal object that is being deformed by collision with the cursor object.

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they appear to be splines extending from the head to the tail.  there may be an underlying bone structure the mouse pushes, which moves the spline's control points. or the mouse  may influence the control points directly.  There's also some dampened spring type motion going on as well.

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