Generalizing is a foundational mathematical practice for the algebra classroom. It entails an act of abstraction and forms the core of algebraic thinking. Kinach (2014) describes two kinds of generalization--by analogy and by extension. This article illustrates how exploration of fractals provides ample opportunity for generalizations of both kinds, which are essential for algebraic reasoning. The activity involved thirty grade 11 students exploring the Koch snowflake as a part of the sequences and series topic in their math course. The primary goal was to enable them to visualize geometric sequences by exploring various patterns in the snowflake construction through pictorial, tabular, and symbolic representations and to make connections among them. The activity provided students with opportunities to engage in explicit as well as recursive reasoning. The importance of such reasoning has been articulated in the Common Core State Standards for Mathematics, which states that students studying algebra in grades 9-12 should be able to "write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms" (CCSS1 2010, p. 21).