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We study the growth at the golden rotation number ω = ( 5 − 1 ) / 2 of the function sequence P n ( ω ) = ∏ r = 1 n | 2 sin ⁡ π r ω | . This sequence has been variously studied elsewhere as a skew product of sines, Birkhoff sum, q-Pochhammer symbol (on the unit circle), and restricted Euler function. In particular we study the Fibonacci decimation of the sequence P n , namely the sub-sequence Q n = | ∏ r = 1 F n 2 sin ⁡ π r ω | for Fibonacci numbers F n , and prove that this renormalisation subsequence converges to a constant. From this we show rigorously that the growth of P n ( ω ) is bounded by power laws. This provides the theoretical basis to explain recent experimental results reported by Knill and Tangerman (2011) [10] . [ABSTRACT FROM AUTHOR]