The authors remark that the Calculus of Variations and Geometric Measure Theory does not seem to have an easy extension to fractal problems. Their aim is to give a contribution to the problem defining lower semicontinuous functionals. They consider the following special case: Let \(V_ 0\) be an equilateral triangle of side length 1 with center in 0, \(V_{h+1}\) the union of \(V_ h\) and \(3\cdot 4^ h\) equilateral triangles of side length \(3^{-(h+1)}\) external to \(V_ h\), such that one of their edges lies on the central third of one of the \(3\cdot 4^ h\) edges of \(V_ h\). Then \(V=\overline{\cup V_ h}\) is the full snowflake whose boundary is composed of three copies of the Koch curve. Let denote \(\partial E\) the topological boundary of the set E and \(\partial^*E\) its essential boundary, that is the set \[ \partial^*E=\{x\in {\mathbb{R}}^ 2:\limsup_{\rho \to 0^+}\frac{| B_{\rho}(x)\setminus E|}{\rho^ n}>0,\quad \limsup_{\rho \to 0^+}\frac{| B_{\rho}\cap R|}{\rho^ n}>0\}. \] If A is any open set and E any set of finite perimeter the authors study the behaviour of the sequence of functionals \[ F_ h(E,A)={\mathcal H}_ 1(A\cap (\partial^*E\setminus \partial^*V_ h))+(3/4)^ h{\mathcal H}_{\alpha}(K){\mathcal H}_ 1(A\cap \partial^*E\cap \partial^*V_ h), \] where \({\mathcal H}_ 1,{\mathcal H}_{\alpha}\) are the 1-respectively \(\alpha\)-dimensional Hausdorff measure \((\alpha =\log 4/\log 3)\) and K stands for the Koch curve. Provided that E is measurable and \((\partial E\cap A)\setminus \partial^*V\) consists of a finite number of regular arcs then the so called \(\Gamma\)-limit of \((F_ n(E,A))\) in the sense of De Giorgi exists and is equal to \[ {\mathcal H}_ 1(A\cap (\partial^*E\setminus \partial^*V))+{\mathcal H}_{\alpha}(A\cap \partial^*E\cap \partial^*V) \] and thus becomes a lower semicontinuous functional.