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In this paper we introduce the strange star product. This product may be used to locate non-infinitely renormalizable unimodal maps f where f | ω(c) is topologically conjugate to an adding machine. Given any sequence α = j 1 , j 2 , · · · , with each j i ≥ 2, the strange star product can precisely construct the kneading sequence of a unimodal map with an embedded copy of the associated α-adic adding machine.doi:10.1080/10236198.2011.608066 fatcat:dig3ruyoqnhdxbl2s43q5rgh6m