While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary interest has recently increased due to pattern-recognition applications in artificial intelligence. Within two empirical studies, we analyze the analogical-transfer capability of primary school students when completing three types of bi-dimensional patterns, namely, numerical, discrete geometric, and continuous geometric. We found that the mechanisms involved in analogical transfer for continuing sequential patterns are based on two complementary cognitive processes: decoding and adapting. In addition, at a basic level of processing, students activate one of the operational tools of shape recognition or counting, and based on it, they find a surface analogy that leads them to use isometric transformations or one-dimensional development for continuing the given pattern. At a more complex level of processing, students activate both shape recognition and counting and are thus able to apply a filter of processing that uncovers a deep-structure analogy, which allows cognitive framing of the problem and leads to coherent 2D developments within the understood conceptual frame. At a more advanced level of processing, students can use a refined filter not only to uncover a deep-structure analogy but also to use an external language to verbalize that analogy, and consequently, to find 2D developments that trigger changes in cognitive framing, showing that pattern generation is a creative activity. Teaching and learning implications are discussed.