The renormalization group (RG) reveals how physical systems look the same at different scales near a critical point. Block-spin decimation on a 1D Ising chain integrates out every other spin, mapping the coupling K → K' = ½ ln cosh(2K). Iterating this map flows toward the trivial fixed point K*=0, while 2D block-spin RG finds a nontrivial critical fixed point.