abstract: An example of a rectiable stationary 2-varifold in \( R^4 \) with non-unique (conical and/or non-conical) tangent varifolds at a point. This answers a question of L. Simon (Lectures on geometric measure theory, 1983, p. 243) and provides a new example for a related question of W. K. Allard (On the first variation of a varifold, Ann. of Math., 1972, p. 460).