Here, we show numerically how thermal resistance in a two-dimensional domain with a point heat source can be reduced with embedded high-conductivity snowflake shaped pathways. The external shape of the domain is square, and its boundaries are heat sink. The geometry of the inserted pathways which corresponds to the minimum T-max was uncovered with the consideration of Constructal Theory, i.e. the constructal design. In the first assembly, number of mother (big) fins was uncovered as the area fraction increases. The results of the first assembly indicate that the increase in number of mother fins does not increase heat transfer after a limit number for the fins. After uncovering the mother pathway geometry corresponding to the minimum T-max the daughter (small) fins inserted at the tip of them, i.e. second assembly. In the second assembly, the fin ratios, small fin location and angle were discovered when the area fraction is fixed. In addition, in the third assembly, larger daughter fins were attached to mother fins. The results of the second and third assemblies document what should be the geometric length scales and the number of daughter fins in order to minimize T-max. The constructal design uncovered is similar to the shape of snowflakes. Therefore, the results also uncover snowflakes correspond to the designs with minimum thermal conductivity, i.e., not mimicking the nature but understanding it with physics. (C) 2018 Elsevier Ltd. All rights reserved.